Aise technical report no 13

Technical Report No. 13 Guide for the Design and Construction of Mill Buildings AISE Subcommittee No. 13 on Design and Construction of Mill Buildings was established in 1962. The Technical Report No. 13 represents an ongoing process of utilizing traditional information and incorpo rating new techniques, standards and products as they become available to provide guidelines for the design, fabrication, construction and maintenance of mill buildings. The guide is organized into six sections and three appendices covering general requirements, geotechnical investigation, loads and forces, foundations, floors and walls, and structural steel.

Purpose

This report serves as a comprehensive guide for owners, engineers, and contractors involved in the design and construction of mill buildings and similar structures It aims to ensure that these buildings are functional, serviceable, economical, and safe Before applying the guidelines to a specific project, it is essential to review each section for relevance and compatibility with applicable regulations and requirements.

Scope

This report provides design information on Class A, B, C, and D mill buildings, as outlined in Section 1.4 It references relevant design guides, codes, specifications, and manuals where appropriate Additionally, it includes insights on conducting thorough site investigations and implementing cost-effective substructure designs.

Classifications of Structures

Mill Buildings, Class A

• Other buildings (as based on predicted operational requirements).

Engineering Drawings and Details

Design Drawings

When cambering is necessary for trusses, beams, and girders, it must be clearly specified Additionally, design drawings for column bases and anchorages should provide all essential information for foundation design, including direct loads, moments, shears, and uplift.

In foundation design, it is essential to specify the allowable bearing pressure, pile loads, pile types, depth, and load test results The design drawings must include clear and sufficient typical details to facilitate the accurate execution of detail drawings, eliminating any ambiguity Additionally, these typical details should clearly indicate the type of connection to be utilized, such as high-strength bolts or welds.

Design drawings, general arrangement drawings, clearance diagrams and erection procedure drawings shall be sent to the owner for approval.

Project Record Drawings

Except as otherwise specified by the owner, the following shall be included:

(1) The location of the building in relation to adjacent property.

(2) The location of permanent benchmarks.

(3) Plumbness of steel work at elevations specified by the owner.

(4) Center-to-center span between runway girders at supporting columns and at mid-span of girders.

(5) Any changes to design shall also be recorded on project record drawings.

Detail Drawings

1.5.5.1 Structural Steel.Such drawings shall be prepared and approved in accordance with AISC specifications (Ref 1) and with the AISC Code of Standard Practice (Ref 2).

1.5.5.2 Concrete Reinforcing Steel.These drawings shall be prepared and approved in accordance with the ACIBuilding Code Requirements for Reinforced Concrete Structures (Refs 5 and 6).

Equipment Installation, Safety, Maintenance and Repair

The owner must provide adequate information to ensure proper installation of equipment, piping, and electrical conduits and trays within the building structure during the cleaning and painting process.

Designated walkways, platforms, stairs, and ladders are essential for maintaining equipment in hard-to-reach areas, with a preference for stairs over ladders when feasible Additionally, it is crucial to implement fall protection and fall restraint measures that comply with OSHA regulations or local authorities.

Repair platforms should be included in building designs to accommodate track wheel changes on EOT cranes.

Escape walkways should be included in building designs to permit emergency exits from crane cabs on hot metal cranes.

Overhead trolley hoists or lifting beams should be strategically installed in the roof structure to facilitate the replacement of heavy crane components The design drawings must clearly specify the lifting capacities of these beams and the allowable loads at hoisting points for maintenance and repair purposes.

Fig 1.1 — Elevation: Typical crane runway clearance diagram.

Clearances

1.5.7.1 Crane Clearance, Related Dimensional and Load Information.Minimum clearances and required dimen- sional information are illustrated in Figs 1.1 and 1.2 A typical crane bridge wheel load and dimension diagram is shown in Fig 1.3.

It shall be the responsibility of the owner to furnish the following information:

(1) Dimensions marked (×) in Figs 1.1, 1.2 and 1.3.

(9) Location of collectors, cable or festoon system.

(10) Lifts, if any, required below floor level.

(11) Desired cab location and elevation of cab floor to suit escape platform (if required), auxiliary access locations, platforms, stairs and ladders.

(12) Size of runway rail, in accordance with AISE Technical Report No 6 (Ref 11).

1.5.7.2 Miscellaneous Clearances.Minimum clearance for medium- or high-voltage cables shall be in accor- dance with governing codes.

Building design must adhere to the clearance standards outlined in railway and highway bridge design specifications Additionally, any other required clearances should be provided as specified by the owner.

Fig 1.2 — Plan: Typical crane runway clearance diagram.

Fig 1.3 — Typical crane bridge wheel load diagram.

Purpose

After a site is considered satisfactory and feasible for use, surface and subsurface exploration, soil drilling and sampling, rock coring and field-testing should be conducted to determine:

(3) Lateral soil pressures for the design of walls.

(4) Subgrade properties for the design of floor slabs on grade.

(5) Recommendations for special and complex soil problems.

(7) The electrical and chemical properties of soil to ensure durability issues of in-ground structures. Simple metal scan for selected parameters may be used.

(8) Site classification for seismic design.

A geotechnical engineer should coordinate the site investigation following the guidelines outlined in Appendix A, primarily focusing on new sites If the owner has already obtained reliable information compliant with these guidelines, only the necessary additional investigations for the project's design and construction should be conducted The findings from the site investigation, along with relevant design criteria, must be documented in the Project Geotechnical Report as advised in Appendix A.

Earthwork

Project Specification

Excavations—Foundations

2.2.2.1 Safety.All excavations shall be conducted and maintained to prevent injuries to the public and to work- ers, in accordance with all provisions of local, state and federal regulations.

2.2.2.2 Support.All excavations shall be performed in a manner that will prevent movement of earth of adjoin- ing sites and structures thereon, including floor slabs, pavements and foundations, utility lines, etc Where dan- ger of undermining adjoining foundations of structures exists, lateral support, underpinning for the foundations, or both, shall be provided.

2.2.2.3 Braced and Open Cut Excavations.Unless soil conditions require braced excavations, all open cut exca- vations shall be performed with adequate safety factors to maintain stable slopes during the construction peri- od and in accordance with design criteria furnished in the Project Geotechnical Report Soil data developed as described in Section A 2.0 shall be furnished by the owner.

In rock excavations, all loose and overhanging rock shall be removed.

Dewatering

after placement of the foundation, provided that it is kept at a level of at least 3 ft below the top of the com- pacted backfill during placement of backfill.

Backfilling Foundations

Backfill materials must consist of clean granular material or cohesive soils, devoid of trash, roots, organic matter, and frozen substances Additionally, nongranulated steelmaking slag can be utilized if it meets the criteria outlined in Section 2.2.5.1 It is essential to avoid placing backfill on surfaces that are underwater, muddy, or frozen.

Backfill must be applied evenly around piers and along both sides of walls, unless the walls are intended for eccentric loading It is crucial to prevent any wedging or eccentric forces that could harm the structures Compaction of the backfill should follow the guidelines outlined in the Project Geotechnical Report at every stage For walls designed as propped cantilevers, backfilling should only commence after the props have been properly installed.

2.2.5.1 Steelmaking Slags.Because of its potential expansion and chemical properties, the use of steelmaking slag as structural backfill is not recommended However, nongranulated steelmaking slag, such as open hearth or basic oxygen furnace slag, may be used in structural fills or as backfill if it is first weathered in accordance with the following procedure to reduce or eliminate its tendency to expand.

Steelmaking slag must be thoroughly soaked with water and stored in controlled stockpiles not exceeding 10 feet in height It should remain moist in these stockpiles for a minimum of six months before use If any further crushing or breakdown of the slag occurs after this initial stockpile period, it must be re-stockpiled and kept moist for an additional six months prior to utilization.

These procedures are not required for processed iron blast furnace slag materials, which are approved as concrete or paving aggregates.

2.2.5.2 Resistant Rock Materials.Because of potential excessive settlements and the difficulty in achieving prop- er placement, the use of rock materials resistant to compaction as structural backfill is not recommended. Although resistant rock can perform satisfactorily as structural backfill when selected, processed and compact- ed as recommended in the Appendix, Section A 3.8, indiscriminate use of these materials can result in serious foundation settlement problems.

Dead Load

The dead load to be assumed shall consist of the weight of all permanent construction and all material and equipment permanently fastened thereto and supported thereby.

Roof Live Loads

The roof must support a minimum live load of 20 psf across its entire horizontally projected surface, accounting for maximum loading conditions In areas with higher snow load requirements due to geographic location, altitude, or local building codes, the highest specified value must be applied Additionally, special considerations should be made for increased snow loads in locations where snow may become trapped, such as valleys or sheds.

Floor Live Loads

Live Load Reduction Factors

100 psf or less, and no reduction factor reducing the load to less than 0.6 of full uniform live load shall be used.

Crane Runway Loads

General

Table 3.1 Recommended Minimum Live Loads, psf

Flux or weigh hopper floors 200

Motor room floors, oil cellar roofs, or similar operating floors 1000

Ore Refining and Material Handling Structures, Sintering and Pelletizing Structures

Boiler house operating floors 250 Miscellaneous walks, access platforms and stairs 100

Vertical Impact, Side Thrust and Traction

(2) 20% of the combined weight of the lifted load and trolley For stacker cranes this factor shall be 40% of the combined weight of the lifted load, trolley and rigid arm.

The lifting capacity of cranes is determined by a safety factor of 10% based on the combined weight of the lifted load and the crane itself In the case of stacker cranes, this safety factor increases to 15% of the total weight, ensuring enhanced stability and safety during operation.

Lifted load refers to the total weight handled by a hoisting mechanism, encompassing the working load along with all associated components such as hooks, lifting beams, and magnets However, it does not include the weight of fixed elements like columns or rams that remain vertically guided during the lifting process.

For pendant operated cranes, the vertical impact, side thrust and tractive forces shall be as follows:

(1) 10% of maximum wheel load for vertical impact.

(2) 20% of maximum load on the driving wheels for the tractive force.

(3) 10% of the combined weight of the lifted load and crane weight for total side thrust.

Radio-operated cranes shall be considered the same as cab-operated cranes for vertical impact, side thrust and traction.

Runway Crane Stops

When designing crane runway girders, it is essential to coordinate the maximum design bumper force with the crane designer, ensuring it is reflected in the structural drawings This design bumper force must not exceed the maximum allowable force on the crane stop to ensure safety and structural integrity.

Moving Loads

Limited Access Vehicles

3.5.1.1 Loads and Impacts due to Railway Equipment.Unless otherwise specified, all floors supporting railroad tracks shall be designed in accordance with Ref 14.

(1) As a minimum, the following impact factors shall be used in the design:

(a) Rolling effect (locomotive only): 10% down on one rail and upward on the other.

(b) Direct vertical effect: 25% of axle load, maximum.

(2) Tractive force—longitudinal tractive force shall be considered in the design of floors supporting limited- access vehicles This force shall be the greater of:

(a) 10% of live load without impact

(b) 15% of weight on the driving wheels.

3.5.1.2 Nonstandard Gauge Equipment.Floors supporting nonstandard gauge trackage provided for floor-oper- ated machines shall be designed for maximum wheel loads, impact and lateral forces as designated by the owner.

Vertical impact shall not be less than 25%.

For nonstandard gauge equipment, the height above the rail for application of lateral traction forces shall be designated.

Unlimited Access Vehicles

TO “Specification for Highway Bridges” (Ref 15) or both.

In addition to the direct vertical loading, the following impact load shall be applied:

(1) Pneumatic-tired vehicles—30% of the wheel load.

Solid-rubber-tired vehicles support 50% of the wheel load, with the tire contact area dimensions and load distribution specified by the owner or according to Ref 15 Additionally, the longitudinal force must be determined either by Ref 15 or by the owner's specifications, depending on the vehicle type.

Track-type vehicles equipped with air hammer attachments carry 25% of the track load, while those used for lifting, scraping, and digging bear the full 100% of the track load It is essential for the owner to provide load data, specify the intended area of usage, and outline the operating procedures.

Contingency Loads

Buildings and structures must be designed to accommodate potential future changes and increases in structural loads, unless directed otherwise by the owner In addition to the loads outlined in Section 3, the design of primary framing members should also consider the potential application of various additional loads.

Floor Beams: One 5000-pound concentrated vertical load applied midspan.

Roof Beams: One 3000-pound concentrated vertical load applied midspan.

Roof Trusses: One 3000-pound concentrated vertical load applied at any single panel point. Platform Beams: One 1000-pound concentrated vertical load applied midspan.

Columns: One 1000-pound concentrated lateral load applied mid-height of any column span, in the weakest flexural direction.

These contingency loads are not cumulative and should be applied to only one member or one panel point at a time.

Special Loads

Guidelines for Vibratory Loading

Vibrating equipment must be engineered to ensure that the lowest natural frequencies of the installed systems—comprising equipment, supports, structures, and soil configurations—are at least 1.5 times greater than the equipment's operating frequency The design of supports for vibratory equipment should encompass a variety of considerations to ensure optimal performance and stability.

(1) Motors and similarly balanced rotating equipment: Vertical impact—25% of the weight of the equip- ment.

(a) Live load—weight of the screen plus a reasonable burden on the screen deck.

(b) Vertical impact—100% of the live load.

(c) Horizontal impact—50% of the live load.

(a) Live load—weight of the pan plus a reasonable burden above pan in hopper.

(b) Vertical impact—25% of the live load.

(c) Horizontal impact—25% of the live load.

(a) Live load—weight of the crusher plus burden.

(b) Vertical impact—100% of the live load.

(c) Horizontal impact—dependent upon individual installation.

(5) Forced or induced draft fans:

(a) Vertical impact—25% of fan weight.

(a) Vertical impact dependent upon installation.

(a) Vertical impact dependent upon installation.

Special Roof-Supported Structures

a part of loads from ducts, ventilators and monitors.

Loads from Mains, Ducts and Pipes

(1) Process piping shall be assumed full for support design.

When designing supports for mains and ducts, it is essential to account for a minimum dust loading equivalent to one-fourth of the duct depth filled Additionally, it is important to evaluate both dry and wet dust densities to ensure optimal performance.

(3) Support for parallel mains and ducts on the same fan system should be designed for an accidentally full condition of any one duct.

Pipe and duct supports must be assessed for load conditions caused by temperature fluctuations and imbalances in internal pressure This evaluation is essential for all systems, including those involving water-cooled ducts and pipes that transport gases, steam, or liquids.

Wind Loads

All buildings and structures must comply with local building codes regarding wind load requirements, taking into account wind speed and exposure criteria as outlined in ASCE 7 or specified by the owner or design engineer Additionally, the design must consider building configurations and production operations that could lead to internal pressure conditions typical of partially enclosed structures.

Seismic Loads and Displacements

All buildings and structures must comply with local building codes regarding seismic forces, displacements, and ductility Site classifications and seismic design categories should follow the local building code or ASCE 7, unless specified otherwise by the owner or the design engineer Additionally, conducting a site investigation is recommended to accurately determine the site classification for seismic design.

In designing structures, it is essential to consider the seismic response interaction with equipment The seismic mass of storage equipment, including tanks, bins, silos, hoppers, and storage racks, must account for the weight of the stored materials during normal operations Conversely, for cranes and trolleys that carry suspended loads, only the empty weight of the equipment should be included in the seismic mass calculations.

In order to ensure that buildings, structures, and equipment remain functional immediately following a design-level earthquake, it is essential to implement design requirements that exceed the minimum standards outlined in the building code.

Load Combinations for Design of Crane Runways and Supporting Structures

Symbols and Notations

The symbols referenced pertain specifically to sections 3.10 and 3.12 of the ASCE 7 Standard, which outlines the minimum design loads for buildings and other structures, and are not applicable to Section 8, which covers symbols.

C vs vertical loads due to a single crane in one aisle only

C ss side thrust due to a single crane in one aisle only

C i vertical impact due to a single crane in one aisle only

C ls longitudinal traction due to a single crane in one aisle only

C vm vertical loads due to multiple cranes

C bs bumper impact due to a single crane in one aisle only at 100% speed

C d dead load of all cranes, parked in each aisle, positioned for maximum seismic effects

L live loads due to use and occupancy, including roof live loads, with the exception of snow loads and crane runway loads

H loads due to lateral pressure of soil and water in soil

T self-straining forces as from temperature changes, shrinkage, moisture changes, creep, or differential settlement

Basis of Design

Axial loads, moments and shears for each type of loading shall be listed separately (i.e., dead load, live load, crane load eccentricities, crane thrust, wind, etc.).

Crane impact loads apply only to runway girders and their connections.

Under repeated loads, allowable stress ranges must adhere to the procedures outlined in Section 5.7, taking into account the estimated number of load cycles based on the building classification specified in Section 1.4 The owner is responsible for increasing the estimated load cycles for any part of the building structure if projected workload changes or potential alterations in building usage necessitate it.

This article outlines load combinations for structural members subjected to repeated loads, specifying that Class A constructions must be designed for 500,000 to over 2,000,000 load repetitions, while Class B and Class C constructions are to be designed for 100,000 to 500,000 and 20,000 to 100,000 repetitions, respectively Notably, these guidelines do not apply to Class D buildings.

The design stress range must remain within the allowable limits defined in Section 5.7 Alternatively, a more advanced method utilizing a variable stress range spectrum can be employed instead of the procedure outlined in Section 5.7.

(1) D + L + (L r or R or S) + C vs + Ci + C ss + C ls (Single Crane)

(2) D + L + (L r or R or S) + C vm + C ss + C ls (Multiple Cranes)

This case applies to all classes of building construction Full allowable stresses may be used.

(2) D + L + (L r or R or S) + C vs + Ci + C ss + 0.5W

(3) D + L + (L r or R or S) + C vs + Ci + 0.67C bs

This guideline applies to all types of building construction, allowing for a reduction of combined load effects by a factor of 0.75, provided that allowable stresses remain unchanged However, it is important to note that no load reduction is permitted when considering only the combinations of dead load and wind.

3.10.2.4 Other Load Combinations.The structural effects of F, H, P or T shall be considered For combinations with or without crane loads, including D + L + (L r or S or R) + (W or E) + T, the total of the combined load effects may be multiplied by 0.67, with no increase in allowable stresses.

Loads on Retaining Walls, Grade Walls and Grade Beams

Loads on Building Foundations

General

This section outlines the essential criteria and procedures for designing foundation components of mill buildings, including soil-bearing column foundations, pile and caisson-supported foundations, grade walls, grade beams, retaining walls, basement walls, slabs on grade, and other necessary concrete elements It serves as a comprehensive guide to ensure a consistently safe design and a cohesive design approach for industrial mill construction.

Concrete Construction

Setting Anchor Rods

If sleeves are used, they shall be completely filled when the base plate is grouted Special care shall be taken to exclude water from the sleeves until grouted.

Soil Bearing Foundations

General

(2) Earth pressures and safety factors for lateral and rotational stability.

(3) Estimated total and differential settlements for various sizes of foundations at different elevations and coefficients for calculation of lateral movements.

(5) Minimum depth of footings for protection from heaving due to frost.

The article discusses the impact of overlapping soil pressures from both existing and proposed structures, including foundations for machinery, floor loads, walls, basement surcharges, and excavations It highlights the influence of vibratory equipment on these pressures and emphasizes the need for ongoing assessments throughout the construction process until all substructures are finalized.

When constructing foundations on nongranulated steelmaking slag, it is essential for the soils engineer to assess the materials for potential expansion properties Additionally, the application of steelmaking slag as fill material must adhere to the guidelines outlined in Section 2.2.5.1.

Using segregated resistant rock for foundation support is generally discouraged due to the limitations outlined in Section 2.2.5.2 If resistant rock material is utilized, it must be installed following the guidelines specified in Appendix, Section A 3.8.

(9) The durability requirements for the concrete.

Ground Water Conditions

To mitigate the effects of soil swelling and shrinking, foundations must be placed below the influence of groundwater Alternatively, support methods such as piles, caissons, or other deep foundation systems should be utilized to ensure stability.

Pile and Caisson Supported Foundations

General

(1) Allowable load capacities and uplift with particular consideration of group effect and minimum spacing between piles.

(2) Allowable total and differential settlement and rotation of the base.

(3) Allowable resistance to lateral forces and coefficient for calculation of lateral movement.

The article discusses the description and impact of current and proposed structures, including walls, floor loads, surcharges, and vibratory equipment It highlights the importance of considering negative skin friction effects when applicable Additionally, it emphasizes the necessity of periodic reviews throughout the contract planning and construction phases of all substructures until completion.

(5) The depth below ground surface to the point of support for evaluation of pile column strength.

(6) Corrosion protection requirements where aggressive substance or electrolytic action can occur in the pile environment Steel piling should not be used for electrical grounding where electrolytic action is possible.

When constructing pile caps or grade beams on nongranulated steelmaking slag, it is essential for the soils engineer to assess the materials for potential expansion properties Compliance with the guidelines outlined in Section 2.2.5.1 is required when utilizing steelmaking slag as fill beneath these structural elements.

Allowable Pile and Caisson Stresses

(Eq 4.1) where: f a = Computed average axial stress in column, ksi f b = Computed average bending stress in column, ksi

F a = Axial stress allowed in the absence of bending moment, ksi

F b = Bending stress allowed in the absence of axial force, ksi

In addition, for prestressed piles: f a + f b + f pe ≤0.45f′c (Eq 4.2) f a – f b + f pe ≥0 (Eq 4.3) where: f pe = Effective prestress after losses, ksi f′ c = Ultimate compressive strength of concrete at 28 days, ksi

Thin-shell concrete piles shall not be used in bending unless properly reinforced and designed as a concrete pile Corrugated shells are not considered as sharing the load.

Steel shells must have a minimum thickness of 0.1 inches and a cross-sectional area that is at least 3% of the gross area of the pile section to qualify as load-bearing Additionally, when a steel shell is incorporated into the design of a pile or caisson, it is essential to account for corrosion allowance when determining the required thickness.

When a section of a pile lacks lateral restraint or the soil conditions do not offer significant support, the strength of the column must be assessed between its support points In contrast, if sufficient support is present, the pile can be considered as continuously supported.

Pipes, tubes and rolled structural piles shall be designed as columns in accordance with AISC Specification, (Ref 1) using the limiting stresses listed in Table 4.1.

Concrete filled steel pipe piles, reinforced concrete piles, prestressed concrete piles, precast concrete piles and reinforced concrete caissons shall be designed by either of the following criteria:

(1) The ACI Recommendations for the Design of Piling (Ref 8) using the limiting stresses listed in Table 4.1.

(2) The ACI Code (Ref 5) In lieu of more refined information, the following load distribution and strength factors shall be used: dead load—10%, live load—90% and capacity reduction factor of 0.7.

When assessing load carrying capacity, any bar reinforcement exceeding 8% of the average cross-sectional area of the pile should be excluded The allowable design stresses for non-reinforced concrete piles, as well as non-reinforced concrete filled shells and tubes with wall thicknesses under 0.1 inches, along with wood piles, must adhere to the maximum stresses specified in Table 4.1 It is important to note that these piles are not suitable for tension use, and the average stress on the section must consistently remain in compression.

Field Control of Pile Driving

4.4.5.1 Driving.The method of driving shall not impair the strength of the pile Shattered, broomed, crumpled or otherwise damaged pile heads shall be cut back to sound material before continuing the driving Where a group of piles is to be driven, a survey should be done after driving to detect horizontal and vertical movements. Piles that have suffered vertical movements, in general, shall be redriven to ensure required capacity Piles that have suffered horizontal movements must be investigated for soundness.

Table 4.1 Allowable Pile and Caisson Design Stresses

Steel: Pipe, tube or shape 0.5 F y or 18 ksi*

Wood: ———— Determined in accordance with ASTM D2899 Tension:

Steel: Pipe, tube or shape 0.50 F y or 24 ksi*

Steel: Tension and compression 0.5 F y or 22 ksi*

Wood: Tension and compression Determined in accordance with ASTM D2899

4.4.5.2 Plumbness.Vertical piles shall not vary more than 2 1 / 2 % from the plumb position, and no pile shall devi- ate more than 3 in in the horizontal dimension from its design location.

4.4.5.3 Records.The contractor shall keep records for each pile driven, giving the designation, tip and cutoff ele- vations, locations, orientation, resistance to penetration for each foot of penetration and resistance to penetra- tion inch by inch for the last 12 in of movement These records shall be submitted to the owner by the contrac- tor in a timely fashion.

4.4.5.4 Load Tests All load tests, required by the soils investigation, shall be performed as per the ProjectGeotechnical Report Unless stated otherwise by the owner, a minimum of two satisfactory load tests should be performed.

Retaining and Basement Walls

Floor Slabs on Grade

Construction and Control Joints

General

Design and workmanship must adhere to the AISC Specification and the AISC Code of Standard Practice, with additional guidance provided in this document When employing Load & Resistance Factor Design (LRFD) methods, the recommendations outlined remain applicable Engineers are encouraged to refer to resources from AISC, AISE, and SSRC for further information and design examples.

Mill Building Framing

Mill buildings are characterized as space frame structures, where planar frames made up of building columns and roof trusses are integrated with a bracing system When an above-grade floor is connected to this framing, its impact must be considered in the structural analysis.

The bracing system plays a crucial role in stabilizing the building's space frame, reducing horizontal movement between cross-bents, and effectively distributing localized crane loads to adjacent bents Additionally, it transmits longitudinal forces, including those from wind, seismic activity, crane traction, and crane bumpers, to the foundations.

The advantages of the space frame versus a planar frame should be utilized in the mill building frame analyses.

In cases where the bottom chord bracing of roof trusses in existing mill buildings is insufficient to support space frame loads, using a planar frame model can serve as an effective alternative to modifying the bracing.

It is recommended that building columns be designed as fixed or partially fixed at the base Percent of fixity depends on anchorage details, foundation and soil parameters.

When calculating localized crane loads on columns, it is essential to distribute the total transverse horizontal side thrust from the crane among the crane runway support columns based on their lateral stiffnesses.

The lateral drift of building frame at the top of crane girders must not exceed 1/400 of the height from the column base or 2 inches, whichever is smaller, under specified load conditions.

(1) Crane lateral forces identified in this report

(2) Building wind loads due to a wind speed that has an annual probability of exceedance no greater than 10% (10-year recurrence interval).

Drift limits can only be surpassed if it is demonstrated that the overall drift will not negatively impact the building's durability or the functionality of its equipment.

According to elastic frame analysis, the crane rail gauge variation caused by gravity loads must remain within +1 inch and -1/2 inch of the specified gauge For snow loads of 30 psf or less, a reduction of 50% is permissible, while snow loads exceeding 30 psf may be reduced by 25%.

The roof trusses at the column lines shall be considered a part of the building frame The frame effect shall be included in the truss member forces.

The truss chord members subjected to local bending shall be analyzed and designed for combined bending and axial stresses.

To ensure structural integrity, primary members and bracing should be connected in a way that their gravity axes intersect at a single point It is essential to account for any eccentricity present in the design of these members to mitigate potential issues.

To ensure effective load sharing between frames, a continuous bracing system must be implemented, extending longitudinally between expansion joints and from the joints to the building's ends This bracing system should be designed according to the calculated loads of the building's space frame Additionally, when roof trusses are utilized, the bracing should be positioned within the plane of the bottom chords.

When interrupting the lower chord bracing system for crane repair facilities or other reasons, a thorough analysis of the impacted bents and bracing is essential.

In roof trusses, intermittent bracing for the top chords may include sway frames or bracing in the plane of the top chords, alongside continuous bracing for the bottom chords It is essential to implement longitudinal bracing to effectively transfer wind, seismic, crane traction, or bumper forces to the foundations, ideally positioned midway between expansion joints or at the midpoint of buildings without them When bracing to column bases is not feasible, the longitudinal force should be proportionally distributed among the effective columns between any two expansion joints based on their stiffness.

Knee braces from the crane girder to the crane runway columns are not recommended.

Lateral restraint for columns and compression chords of trusses and girders is achieved when the bracing system is engineered to withstand a transverse force equivalent to 2.5% of the resultant compressive axial stress multiplied by the area of the compressed flange or chord.

In furnace buildings and similar structures that manage hot metal and experience significant temperature fluctuations, transverse expansion joints should be installed at intervals of about 400 feet For buildings that do not encounter wide temperature variations, the recommended spacing between transverse expansion joints is approximately 500 feet.

Buildings with multiple aisles must include appropriate longitudinal joints If the building width surpasses 500 feet or consists of more than five aisles, it is essential to incorporate longitudinal expansion joints.

Long buildings and runways that extend perpendicular to the axes of adjacent structures should not be rigidly connected unless specific measures are implemented to accommodate movement or expansion This ensures that the alignment of one structure is not adversely affected by the other.

5.7 Allowable Stress Range under Repeated Loads (7.14)

Roof Trusses

The roof trusses at the column lines shall be considered a part of the building frame The frame effect shall be included in the truss member forces.

The truss chord members subjected to local bending shall be analyzed and designed for combined bending and axial stresses.

To ensure structural integrity, primary members and bracing should be connected in a manner that aligns their gravity axes at a single intersection point In cases where eccentricity is present, it is essential to account for its effects during the design process of the members.

Bracing System

For effective load sharing between frames, a continuous bracing system must be implemented, extending longitudinally between expansion joints and from expansion joints to the building's ends This bracing system should be designed based on the calculated loads of the building space frame Additionally, when roof trusses are utilized, the bracing must be positioned within the plane of the bottom chords.

When interruptions occur in the lower chord bracing system, whether for crane repair facilities or other reasons, a thorough analysis of the impacted bents and bracing is essential.

Continuous bracing is essential for the bottom chords of roof trusses, while intermittent bracing, such as sway frames, may be applied to the top chords To effectively transfer wind, seismic, and crane forces to the foundations, longitudinal bracing should be strategically positioned midway between expansion joints or at the midpoint of buildings lacking these joints When direct bracing to column bases is not feasible, the longitudinal force must be proportionally distributed among the effective columns between expansion joints based on their stiffness.

Knee braces from the crane girder to the crane runway columns are not recommended.

Lateral restraint for columns and the compression chords or flanges of trusses and girders is achieved when the bracing system is engineered to withstand a transverse force equivalent to 2.5% of the resultant compressive axial stress multiplied by the area of the compressed flange or chord.

Expansion Joints

In furnace buildings and similar structures that manage hot metal and experience significant temperature fluctuations, it is essential to install transverse expansion joints at roughly 400-foot intervals For buildings not exposed to extensive temperature variations, these joints should be spaced approximately 500 feet apart.

For buildings with multiple aisles, it is essential to incorporate longitudinal joints as necessary Specifically, if the building's width exceeds 500 feet or consists of more than five aisles, the installation of longitudinal expansion joints is required to ensure structural integrity.

Long buildings and runways should not be rigidly connected to adjacent structures unless specific measures are implemented to accommodate movement or expansion, ensuring that misalignment does not occur between them.

Allowable Stress Range Under Repeated Loads

When determining the allowable stress range for repeated loads, it is essential to treat all steels uniformly, regardless of their varying yield points Structural members and fasteners must be designed to ensure that the maximum design stress range remains within the allowable fatigue stress range for repeated loads, as outlined in the most recent AISC Specification for Structural Steel Buildings For loading conditions, refer to Table 5.1.

Crane Runway Girders

General

Building Class Loading Condition Number of Loading Cycles

(a) About 1 application per day for 50 years

(b) About 5 applications per day for 50 years

(c) About 25 applications per day for 50 years

(d) About 100 applications per day for 50 years

When analyzing the rail-to-top-flange interface, it is crucial to consider the impact of torsional moments and out-of-plane forces, which encompass lateral wheel loads on the rail head and the eccentricity between the rail and the girder web's centerline This eccentricity arises from the combined construction tolerances and the horizontal slip permitted by the rail clips A precise analysis and design solution for these factors is intricate and exceeds the limits of this document.

It has been found through experience that, for members designed and constructed in accordance with the recommendations contained in this report, satisfactory performance can be expected without additional strengthening.

Crane girders must be designed, detailed, and fabricated to withstand fatigue damage In all building classes, a full penetration weld with contoured fillets is required between the web and top flange, except where specified otherwise For building classes C and D under Loading Condition 1, continuous fillet welds are permissible if they are engineered to support the full applied loads, including the local effects of individual wheel loads It is essential to account for fatigue effects when there are over 100,000 cycles of individual wheel loads, as well as the impacts of torsional moments and out-of-plane forces.

Bottom flanges may be welded to web plates with fillet welds, provided they are continuous welds on both sides of the web.

Web and flange plate splice welds must be complete penetration butt welds, ensuring structural integrity All flange plate splice welds should be ground flush on all sides and edges, with grinding aligned parallel to the girder span Intermittent fillet welds are prohibited, except for cover plate and stiffener welds on girders designed for pendant controlled cranes operating under Loading Condition 1 in Building Classes C and D.

There shall be no welded attachments to the bottom flange of the crane girder.

Stress Calculations

When trusses are used in lieu of runway girders, local bending stresses between panel points and second- ary stresses shall be included in the stress computations.

Stresses due to simultaneous vertical and lateral loadings shall not exceed the requirements as specified herein.

5.8.2.1 Rolled Shapes and Built-up Single Web Plate Girders Having an Axis of Symmetry in the Plane of Their Web (7.15.1).In the design of single web girders, the following interaction formula shall be satisfied:

The computed average axial stress (f a) is measured in ksi, along with the computed stress due to the bending moment about the X-X axis (f bx) and the computed stress due to the bending moment about the Y-Y axis (f by), both also expressed in ksi.

F a = Axial stress allowed in the absence of bending moments, ksi

F bx = Allowable stress for bending about the (X-X) axis, ksi, as specified in Ref 1

F by = Allowable stress for bending about the (Y-Y) axis, ksi, as specified in Ref 1

Stresses in the tension flange should be based on the net section moment of inertia, considering only the vertical loads.

5.8.2.2 Girders with Backup Bracing Systems.Each web system shall be assumed to take the loads imposed thereon, with no more than a width of of flange plate adjacent to each side of a vertical web included in calculating the section properties.

NOTE: F y = Specified minimum yield stress of steel, ksi t f = Thickness of beam or girder flange, in.

When a flange is continuously connected to a thinner auxiliary plate that is nearly in the same plane, the effective width of this thinner plate in relation to the flange must not exceed a specified limit.

(Eq 5.2) where: w e = Effective width of auxiliary plate t a = The thickness of the auxiliary plate, in. b f = The overall width of the plate, in.

For combined vertical and transverse loads, it is essential to adhere to interaction Equation 5.1, with the condition that F bx represents the full allowable stress for bending in built-up members where the compression flange is laterally braced The resistance to transverse loads is assumed to be provided by a horizontal girder formed by the entire top flange of the box system, functioning as the web, limited to no more than half the vertical plate or the depth of the vertical web.

(Eq 5.3) where: t w = thickness of beam or girder web (in.) (see Fig 5.1) d w = effective depth of the vertical web

5.8.2.3 Box Girders with Transverse Diaphragms (7.15.2) In the case of the closed box sections with cross- diaphragms or X-bracing designed to distribute local loads to flanges and webs, the complete cross-section may be assumed to resist the combined vertical and lateral loads Shear stress due to torsion and bending shall be included Width-thickness criteria for compression of shear members shall be met.

Web Thickness

(Eq 5.4) where: h = clear depth of web between flanges, in.

The allowable bending stress (Fb), measured in ksi, is specified in Section F1.1 of the AISC Specification However, if longitudinal stiffeners are utilized, the design must adhere to the guidelines outlined in AISE Technical Report No 6.

Bottom Flange Bracing

Vertical cross-frames should only be utilized if the frame and stiffening truss are engineered to handle the imposed forces, taking cyclic considerations into account Additionally, lacing must be designed to withstand a minimum force of 2.5% of the axial force in the bottom flange at mid-span, and it is important to note that lacing should not be welded to the bottom flange of the crane girder.

Stiffeners

Intermediate stiffeners must be welded to the top (compression) flange using a full penetration (beveled) weld, ensuring they do not extend to the bottom (tension) flange In contrast, end bearing stiffeners require full penetration (beveled) welds to both the top (compression) and bottom (tension) flanges Alternatively, these end bearing stiffeners can be welded solely to the bottom flange to achieve full bearing support.

All welds connecting stiffeners to web plates or flange plates must be continuous, except for building classes C and D, where intermittent fillet welds can be utilized for the intermediate stiffener-to-web connections Additionally, stiffeners should feature clipped corners to ensure adequate clearance for the web-to-flange welds.

If is equal to or greater than 70, intermediate stiffeners shall be required at all points where:

(Eq 5.5) where: f v = The greatest unit shear stress in the panel under any condition of complete or partial loading, ksi

The allowable shear stress shall be as specified by the latest AISC Specification (Ref 1).

The clear distance between intermediate stiffeners, when stiffeners are required by the foregoing, shall be such that the smaller panel dimension a or h shall not exceed: f h t v w

Fig 5.1—Areas assumed effective as per Sections 5.8.2.2 and 5.8.4.

(Eq 5.6) where: a = Clear distance between transverse stiffeners, in. h = Clear distance between flanges, in.

Intermediate stiffeners shall be applied in pairs, one on each side of the web Intermediate angle stiffeners may be crimped over the flange angles.

Intermediate stiffeners are essential for stabilizing the web plate against buckling rather than transferring concentrated loads from the flange to the web These stiffeners must be constructed from a section that meets or exceeds the specifications outlined in the relevant formula.

I s = Moment of inertia of the pair of stiffeners about the centerline of the web, in 4

Local Wheel Support

Ensure that the project does not exceed 1/32 inch above the back of the flange angles If full bearing is not achievable, the design of the top flange fastening to the web must accommodate the entire wheel load concentration, which should be distributed over a distance equal to twice the depth of the crane rail section, in addition to the gauge distance to the top line of fasteners.

In welded plate girders, wheel load concentrations are transmitted to the girder's web plate through the web-to-flange weld When calculating the force per unit length, it is essential to assume that the wheel load is distributed over a distance that is double the total depth of both the crane rail and the girder flange thickness.

Deflection

Columns

General

or intermittent vertical diaphragms shall have the connecting segments and their connections designed to pro- vide integral behavior of the combined column section.

Columns featuring intermittent vertical diaphragms or diagonal lacing must have their shafts designed to accommodate forces such as shear, axial loads, and bending moments, as determined by frame analysis Additionally, it is essential to consider the impact of out-of-plane bending in columns resulting from the longitudinal eccentricity of crane girder reactions.

Brackets

Where crane girders are supported on brackets, impact shall be included in the bracket design and its con- nection to the column.

Floor Framing

When designing floors for vibrating machinery, it is essential to ensure that both the floors and their supporting frameworks are rigidly braced in horizontal and vertical planes Special attention must be paid to minimize vibration and maintain alignment in the design of these structures Additionally, the owner must provide the necessary tolerances required by the machinery.

Side Wall and Roof Framing

When designing light-gauge purlins and girts, it is essential to adhere to the AISI "Specifications and Commentary for the Design of Light Gauge Cold-Formed Steel Structural Members." Additionally, it is crucial to account for corrosion in the design of secondary members whenever relevant.

Girts shall be connected with a minimum of two bolts at each end.

Depth Ratio

The following ratios of depth to length shall be used as a guide:

(2) Beams supporting floors for vibrating machinery and track—1:16

(3) Rolled beams and girders for ordinary floors and rafters—1:24

(4) Roof purlins and gable columns—1:32

(6) The outstanding legs of tension members having a slope of 45 degrees or less with the horizontal shall be not less than 1 / 90 of the unsupported length.

Minimum Thickness of Material

The minimum thickness of material exclusive of secondary members such as purlins and girts shall be:

The mean thickness of the flanges will be used to control the thickness of rolled shapes, irrespective of the web thickness Additionally, any metal that is subject to significant corrosive conditions must be adequately protected against corrosion, as per the owner's specifications.

Connections

Shop and field connections may be riveted, welded or bolted.

Unfinished bolts (A307) are suitable for use in shop and field connections of Class D buildings that do not have crane runways or significant vibrating equipment They can also be utilized for connecting secondary members, including purlins, girts, door and window framing, and temporary bracing For all other bolted connections, it is essential to use pretensioned high-strength bolts.

For members exposed to fatigue cyclic loading or vibrations, slip critical-type high-strength bolted connections are essential In other instances, pretensioned high-strength bolts can be utilized for bearing-type connections, as indicated in the drawings.

Appurtenant material shall not be attached to structural members unless added to drawings as a revision and approved by a qualified engineer.

Spacing of Bolts and Welds

In general, bolted and welded details shall conform to requirements of the AISC Specification except as noted herein.

When connecting the crane runway girder to the horizontal diaphragm, ensure that the bolt spacing does not exceed the minimum required for effective shear transfer, adheres to AISC intermittent attachment standards for compression members, or exceeds 8 inches—whichever is the most restrictive Additionally, if the connection involves a welded horizontal diaphragm, a continuous weld is mandatory.

Crane Rails and Joints

Bolted Rail Joints

All bolted rail joints must be tightly fitted to ensure that the gap between rail ends does not exceed 1/16 inch It is essential to stagger the joints across the runway, avoiding alignment with the crane's wheelbase, and they should not be positioned at the ends of crane girders Additionally, rail lengths should be a minimum of 10 feet.

Inspection and Quality of Welds

Tolerances

Column Base Lines

Base Plates

be level within 0.01 in across length or width.

All columns must maintain consistent tolerances for bay and aisle widths, ensuring that two base plates used as the foundation for a built-up column section are aligned at the same level, with an overall tolerance of 1/16 inch.

Crane Runway Girder Fabrication Tolerances

5.18.5.1 Crane Girders.Horizontal sweep in crane runway girders shall not exceed 1 / 4 in per 50-ft length of gird- er spans Camber shall not exceed ± 1 / 4 in per 50-ft girder span over that indicated on the design drawings.

Fig 5.2—Typical fabrication and erection tolerances.

5.18.5.2 Girder Ends.At the ends of the girder supported by the columns, the bottom flange shall be flat and perpendicular to the web The flatness tolerance shall be ± 1 / 32 in at any point supported by the column cap plate The perpendicularity of the web to bottom flange shall be less than ± 1 / 64 in per foot of flange width.

5.18.5.3 Girder Depths.Depths of crane girders shall be detailed and fabricated to a ‘KEEP’ dimension at their ends of ± 1 / 32 in by use of a variable thickness sole plate.

Crane Girder and Rail Alignment

be aligned horizontally to within ± 1 / 4 in of the theoretical base line both sides of the runway.

Crane rail centers must not deviate more than ± 1/4 inch from the theoretical dimensions indicated in the drawings, adjusted to a temperature of 68°F Additionally, the horizontal misalignment of crane rails is limited to a maximum of 1/4 inch for every 50 feet of runway, with an overall maximum deviation of 1/2 inch from the theoretical location.

Vertical misalignment of crane rails shall not exceed 1 / 4 in per 50 ft of runway with a maximum of 1 / 2 in total deviation from theoretical location.

Crane rails shall be centered on crane girder webs whenever possible In no case shall the rail eccentricity be greater than three-fourths of the girder web thickness.

Tolerances

Fig 5.3—Typical crane col- umn fabrication tolerances.

Purpose

This commentary aims to enhance and clarify specific sections of the report that are not addressed in other parts References to the report will be made using the corresponding paragraph numbers.

Classification of Structures (1.4)

Although a classification A, B, C or D is applied to the entire structure, it should be recognized that only a rela- tively small portion of the structure usually will be affected.

Crane girders and their supports, which sustain many repetitions of loading, are representative of those por- tions of the building to which the classifications apply.

Clearances (1.5.7)

For new buildings, it is essential to maintain a minimum clearance of 18 inches between the column faces and the ends of the crane's truck to ensure safe passage for personnel However, if alternative egress routes that do not require movement between the column and crane are available, the 18-inch clearance can be waived, allowing for reduced space while still ensuring safety.

Roof Live Loads (3.2)

A minimum live load recommendation of 20 psf is essential for ensuring structural rigidity across all horizontally projected surfaces, even in areas without expected snowfall In regions where annual snowpack leads to roof snow loads exceeding 20 psf, it's crucial to consider these higher loads and refer to ASCE 7 for snow load distribution coefficients This reference includes a snow map that offers valuable information for the entire United States Additionally, in mountainous areas, local conditions and historical data should guide the determination of specific loading requirements.

Crane Runway Loads (3.4)

General (3.4.1)

Static loads in cranes refer to the weight of components such as the bridge, trolley, and lifting mechanism, along with the lifted load itself, all of which are provided by the manufacturer and contribute to the rated vertical wheel loads In contrast, dynamic loads arise from the crane's operations, including vertical impacts, horizontal side thrusts, and tractive forces during load lifting, trolleying, and crane travel These dynamic loads are influenced by the inertia of both the crane components and the lifted loads during acceleration and deceleration across all functional movements.

The analytical assessment of crane dynamic forces must account for the interaction between the mill building and the crane, which occurs along the crane runway In real-world applications, the likelihood of these instantaneous forces occurring simultaneously is very low.

To assess the dynamic forces of existing mill buildings, a field crane test method can be employed, simulating the most extreme operational conditions to generate maximum impact and side thrust forces By installing a system of strain gauges on the crane runway girders and the crane itself, it becomes possible to measure stress fluctuations caused by different crane activities These recorded strains can then be converted into stresses, allowing for the calculation of the resulting forces.

Vertical Impact, Side Thrust and Traction (3.4.2)

When upgrading existing mill buildings, it's important to consider that using the load factors outlined in paragraph 3.4.2 may lead to overly cautious crane loadings For detailed guidance on upgrading existing structures, please refer to Appendix C of this report.

Crane Runway Stops (3.4.3)

The energy absorption device (e.g., hydraulic or spring) shall be designed/selected to satisfy the following cri- teria:

(1) The deceleration rate for the bridge shall not exceed 16 ft per second squared at 50% of the full load rated speed or at 50% of the maximum attainable speed, if known.

(2) The device shall be capable of absorbing the energy at 100% of the full load rated speed.

(3) The maximum force generated by the device shall be less than maximum allowable force on the run- way stop.

The design of the building, end stops, and their connections must ensure they can withstand forces generated at 100% of the full load rated speed, with a recommended 50% increase in allowable stresses for this scenario To calculate the energy absorption requirements for bridge bumpers, the trolley should be positioned in the end approach to maximize end reactions from both the bridge and trolley This maximum end reaction will determine the weight impact on each bridge bumper, while the bumper's energy-absorbing capacity is based on a "power off" condition, typically excluding any lifted load that may swing freely.

For new construction, careful attention to reductions in bumper end force can produce cost savings in run- way girders, end stop and support structure designs.

Bumper suppliers must provide certification verifying the performance of their proposed bumpers Additionally, the height of the bumper above the top of the rail should be coordinated with or determined by the crane manufacturer to ensure compatibility and safety.

Fig 7.2 shows basic calculations for hydraulic and spring bumpers.

Vibration (3.7.1)

Rotating and vibrating equipment should be designed to minimize excessive vibration levels Examples are:

Fig 7.1—Location of total inertia force of crane.

Compressors and similar equipment experience dynamic loads during normal operations, making them vulnerable to wear and potential failure due to excessive vibration It is essential to evaluate both equipment structure interaction and soil structure interaction, especially for installations in rigid buildings, to ensure the integrity and longevity of the supporting structures.

Equipment specifications should give the desired relationship between the lowest natu- ral frequency of the equipment and the operat- ing frequency.

Wind Loads (3.8)

Most jurisdictions in the U.S base their build- ing code on one of the model building codes.

Wind load provisions in various codes are primarily based on ASCE 7, while also adhering to the specific limitations and requirements of local regulations In Canada, it is essential for structures to comply with the National Building Code.

For flexible buildings or structures, a dynam- ic analysis of wind loads may be appropriate or even required by code.

Investing in wind tunnel model tests is beneficial for structures that face significant costs associated with failure or overdesign, as these tests provide a more precise assessment of both static and dynamic wind behavior.

Seismic Forces (3.9)

When assessing the need for seismic design in structures, it's crucial to recognize that significant earthquakes can occur beyond the western United States While eastern regions experience earthquakes less frequently, they can still be severe, necessitating consideration in the design process.

Design engineers must recognize that real earthquakes involve dynamic displacement loading rather than merely static force loading, as suggested by simplified building code calculations These calculations often underestimate actual forces and depend heavily on structural ductility that exceeds typical expectations.

Fig 7.2—Hydraulic Crane Bumper, Runway End Stop Example

Bridge weight, W B = 200 kips Bridge full load rated speed, V B = 6 ft per second Trolley weight, W T = 40 kips

Impact weight per side (load free to swing),

Allowable deceleration (per AISE TR 6):

A 50% ≤16 ft/sec 2 @ 50% speed For deceleration at 50% of full load rated speed:

Stroke must be at least ((V 50% ) 2 (12”))/(2*A 50% ) Stroke must be at least

Deceleration force must not exceed (W e /g) * A 50%

Deceleration force must not exceed

The stroke measurement of 3.38 inches is based on a fully efficient bumper and should be adjusted according to the actual efficiency of the bumper used Bumper efficiency can differ significantly depending on the type and design, with typical hydraulic bumpers achieving around 80% efficiency, while coil spring bumpers only reach about 50% For instance, if a hydraulic bumper operates at 80% efficiency, the stroke must be increased accordingly to ensure optimal performance.

For energy absorption at 100% of full load rated speed:

Kinetic energy K E to be absorbed

The end force F e is inversely proportional to the stroke, S B , and to the efficiency, E B , of the bumper,

For example, a bumper with maximum stroke of 10 in and 80% efficiency would generate a force of:

To meet the maximum allowable force of 100,000 lb on the runway stop, the bumper supplier must develop an optimal combination of energy absorption, stroke, and efficiency Additionally, the bumper must ensure adequate deceleration at 50% of the full load rated speed.

For end force not to exceed 100,000 lb, the bumper stroke would be adjusted as follows:

Therefore, for this example, an acceptable hydraulic bumper at 80% efficiency will have the following characteristics: minimum stroke length = 11.4 in. maximum end force at 100% speed = 100 kips

in. yield displacement of the structure in order to absorb the energy of the structure’s response to an earthquake.

It is essential to follow the building code detailing requirements for each construction material in order to pro- vide a safe and ductile structure.

Load Combinations for Design of Crane Runways and Supporting Structures (3.10)

Case 1 Load Combinations (3.10.2.1)

In crane runway upgrade projects, engineers can apply the damage accumulation principle in fatigue-related analyses for structures experiencing variable amplitude loadings For further details and examples of crane runway fatigue analyses, refer to Reference 34.

Soil Bearing Foundations (4.3)

Mill buildings can typically accommodate minor differential settlements of about 1 to 1.5 inches However, larger settlements may lead to operational challenges, particularly for cranes, which may experience drift during essential tasks like teeming.

In addition, large differential settlements can cause stress problems in the structure depending on its flexibil- ity and connectivity.

In planning the foundation for a mill structure, the engineer should consider but not be limited to the follow- ing:

• Variations of the compressible strata in the area of the structure.

• Surcharge effects of equipment or material storage.

• Combinations of different types of foundations as well as spread footings at different elevations.

Each of these might cause differential settlement and might be a reason for changing foundation to piling or other construction.

Expansion Joints in Floor Slabs on Grade (4.6.7)

Use of expansion joints in floor slabs is not recommended due to the possibility of differential settlement between adjacent slabs.

Column and Truss Bents (5.9.1)

Columns consisting of multiple shafts interconnected by intermittent diaphragms, such as battens or lacing bars, must be designed to function as a cohesive unit When a continuous longitudinal web plate connects these shafts, the moment of inertia of the entire solid section can be utilized for frame analysis.

Building Expansion Joints (5.6)

Expansion joints shall preferably be constructed of two (2) independent column shafts.

Allowable Stress Ranges Under Repeated Loads (5.7)

Under cyclic loadings, members, fasteners or weld metal may ultimately develop fatigue cracks, which may lead to structural failure.

This section aims to prevent structural failure by establishing stress limitations that account for local stress concentration and load cycle frequency The latest North American fatigue provisions utilize equations to calculate the design stress range based on the selected design life, excluding loading conditions Designers are responsible for estimating the expected number of full load cycles or their equivalent through load spectrum analysis or cumulative fatigue damage assessment For guidance, loading conditions are included in this report when more specific information is unavailable.

Crane Runway Girders (5.8)

Rolled Shapes and Built-up Single Web Plate Girders Having an Axis of Symmetry in

This section focuses on open section girders where lateral-torsional buckling must be accounted for in the design To assess the compressive stress in the top flange under simultaneous vertical and lateral loads, Equation 5.1 offers a transition formula The stress resulting from lateral load should be calculated based on the sectional properties highlighted in Fig 7.3a, specifically around the (Y-Y) axis, utilizing a modified lateral load Q (eff) as illustrated in Fig 7.3b Importantly, the allowable bending stress due to the lateral load F does not require reduction, and the substitution of Q (eff) for Q is not mandatory for fully boxed members.

The use of Eq 5.1 applies to Case 2 loadings only In checking for adequacy under repeated loads, for Case

1 loading, lateral buckling need not be a consideration.

Unsymmetrical Built-up Members and Closed Section Girders Without Diaphragms along

In structures with only one or two cross-braces or diaphragms, there is an inadequate provision for the continuity of integral box action, as detailed in Section 5.8.2.3.

This section outlines the provisions illustrated in Fig 5.1, indicating that Eq 5.1 can be utilized without concerns of lateral buckling For Case 2 loadings, where F bx and F by equal 0.6F y, the equation simplifies to a verification of maximum combined stresses, represented as f bx + f by ≤ 0.6F y (Eq 7.1).

The maximum combined stress from vertical and lateral loading occurs at the upper left corner of the cross-section, resulting in compression When calculating the bending stress (f bx) due to vertical load, it is essential to consider the effective section properties of the area formed by the diagonal and horizontal crosshatched portions, as outlined by the AISC.

Specification allows for a significant width-to-thickness ratio in compression, particularly for the flange segment on the left side of Fig 5.1 To the right, the empirical equation from Section 5.8.2.2 applies, which addresses allowable ratios when both longitudinal edges of a compression plate are supported This equation is adjusted to account for variations in thickness and acknowledges that only one side of the girder is effective in the absence of regularly spaced intermittent diaphragms When calculating the effective area for resisting horizontal loads, the section properties of the diagonally and vertically crosshatched portions must be considered Additionally, the compression flanges are supported against lateral buckling by either the main girder or backup truss, depending on the thrust direction.

Fig 7.3—Effective side thrust and effective area resisting side thrust in open section girders.

Bottom Flanges Bracing (5.8.4)

7.15.3 Bottom Flange Bracing (5.8.4).Although a horizontal truss bracing system is often used to stiffen the tension flange of the crane girder, such a stiffening truss, unless accompanied by cross-bracing at frequent inter- vals, does not prevent vertical differential deflection of the crane girder with respect to the auxiliary backup truss or adjacent crane girder of interior aisles For additional information, see Section 7.15.

Load Wheel Support (5.8.6)

7.15.3 Bottom Flange Bracing (5.8.4).Although a horizontal truss bracing system is often used to stiffen the tension flange of the crane girder, such a stiffening truss, unless accompanied by cross-bracing at frequent inter- vals, does not prevent vertical differential deflection of the crane girder with respect to the auxiliary backup truss or adjacent crane girder of interior aisles For additional information, see Section 7.15.

7.15.4 Stiffeners (5.8.5) Bearing stiffeners designed by AISC specifications are designed essentially as columns Buckling is prevented in the plane of the web, and the application of the column formula need be applied only for buckling normal to the plane of the web.

Previously, intermediate stiffeners were not welded to the top flange and were typically designed as tight fits, leading to a gap that allowed the top flange to rotate around its longitudinal axis with each crane movement This rotation, combined with the local effects of crane wheel loads, resulted in fatigue cracks in the web after less than 1,000,000 cycles Laboratory studies have demonstrated that welding the stiffener to the underside of the top flange significantly reduces web stresses, thereby enhancing fatigue life Alternative methods to limit this rotation are also acceptable For further insights and test findings, refer to the ASCE Journal of the Structural Division, Vol 102, No ST5, May 1976.

7.15.5 Local Wheel Support (5.8.6).Previous editions of this report included a formula for computing these stresses This formula was based on several assumptions that led to results that have been shown to be con- servative by a factor of approximately 4 The recommendation for including this stress in design calculation has been deleted from this report because the actual magnitude of these stresses is insignificant for these types of structures.

Extensive research on localized wheel load effects was conducted in Europe and the U.S from the 1960s to the 1980s, with significant studies led by various steel producers in the U.S These studies yielded important recommendations, such as utilizing full-penetration welds for web-to-flange connections, implementing deep copes on vertical stiffeners, and securing the stiffeners to the bottom of the compression flange with full-penetration welds.

Columns (5.9)

Columns with a Continuous Web Plate Between Building and Crane Column Elements

In analyzing the lower segment for bending around the y-y axis, it is conservatively assumed that the crane column element fully resists the bending caused by the eccentricity of crane girder reactions The amplification of the axial stress (f) due to deflection is influenced solely by the average axial stress (f′ a) in the crane column element This stress (f′ a) is calculated by adjusting the average stress from the moment about the x-x axis, measured at the centroid of the crane column element, by adding or subtracting it from the overall average stress (f a) of the lower segment's cross-section.

The allowable axial stress, denoted as F_a, is determined under axial load and can be influenced by the buckling of a stepped column about the x-x axis, calculated using the equivalent length KL/r_x Alternatively, it may be assessed based on buckling about the y-y axis, depending on the unsupported length of the column In the case of monosymmetrical columns, the stress considerations involve both the crane and building column elements.

F F a a mx bx a ex bx my by a ey by

When analyzing different sections, it is essential to consider both flexural-torsional and torsional buckling of the entire section, as outlined in Reference 1, paragraph E3, and Reference 35, Appendix E For equations 7.3 and 7.4, the minimum values of F_a should be utilized.

For bending in the plane of the bent about (X-X), a value of 0.85 for C mx is recommended when all bents experience simultaneous wind load and side sway is assumed In contrast, when evaluating a single bent under maximum crane loading without wind (Case 2 loading), a value of 0.95 for C mx should be used These specified values of C mx apply solely to the lower segment.

C my In determining this coefficient, as well as values of all other parameters in the third term of

In the analysis of the crane column element, it is assumed to be effective only at its top (B), where it is not rotationally restrained but is supported against longitudinal joint translation Despite the lack of restraint, bending from eccentric loading may occur at point B Typically, the base (C) is considered fixed unless poor footing conditions are present If there is no interaction with the building column, half of the moment at B from unequal reactions on adjacent girder spans will transfer to the base, resulting in C my = 0.4 If base fixity at C cannot be assumed, then C my should be adjusted to 0.6 for hinged conditions or interpolated between 0.4 and 0.6 The maximum compression stress due to bending about the X-X axis in the crane or building column elements is denoted as f bx, while f by represents the maximum compression stress due to bending along the Y-Y axis in the crane column element.

In the context of crane or building column elements, the allowable extreme fiber stress due to bending, denoted as F bx, may need to be reduced below 0.6F y due to insufficient lateral support This allowable stress reduction can be determined based on the axial stress of the crane column element acting as a column in bending about the (Y-Y) axis, which corresponds to the (X-X) axis of the individual crane column element in the steel shapes manual for rolled sections The calculated allowable column stress should be adjusted by the ratio c m /c c as specified in Section BB of the relevant figure Ultimately, if the resulting stress exceeds 0.6F y, the value of F bx should be taken as the smaller of the two stress values.

The bending component related to the weak axis of the combined crane and building column elements does not require a reduction in allowable stress for lateral buckling Additionally, as the bending resistance is attributed solely to the crane column element of the lower segment, the allowable stress for a compact section can be utilized, provided that the criteria outlined in Section F1.1 of Reference 1 are satisfied.

The stress used to determine the amplification of column deflection in bending should be based on the equivalent length of the entire stepped column, similar to the approach for F a when bending occurs about the x-x axis.

When considering the crane column element, if the base is assumed fixed, use a value of K = 0.8; otherwise, set K = 1.0 The length used to determine KL should correspond to the crane column element BC.

Laced or Battened Columns

The maximum axial compression stress in crane or building column elements is determined by the axial forces acting on the members and their cross-sectional areas For crane column elements, the axial compression stress is equal to the maximum stress (f′ a = f a), while for building column elements, the corresponding stress is zero (f′ a = 0).

The allowable stress under axial load, denoted as F_a, must be calculated individually for each column element, taking into account the slenderness ratios (KLx/rx and KLy/ry) concerning both strong and weak axes Typically, the crane and building column elements are designed as doubly symmetrical sections, eliminating the need for flexural-torsional buckling checks.

Cmx and Cmy are bending coefficients for crane column elements, defined in relation to the combined column section's strong and weak axes, paralleling the definitions used for columns featuring a solid web plate.

The value of C mx is 0.85 for building column elements, indicating the maximum compression stress (f bx) experienced in the crane or building column due to bending along the strong axis (x-x) of the combined column section Additionally, the maximum compression stress (f by) in the crane column element arises from bending along the weak axis (y-y) of the combined column section.

The allowable compression stress for individual column elements results from bending around the strong axis of the combined column Typically, this bending occurs in the lower segments of separate column elements, specifically between the connection points of the battens or diagonals to the crane or building segment.

F by The allowable compression stress due to bending of the crane column element about the weak axis of the combined column section.

The unbraced lengths for lateral support along the x-x and y-y axes of the lower segment are essential for determining the F bx and F by values for each column element, in accordance with AISC recommendations.

F′ ex and F′ ey Same as for the columns with a solid web plate.

Web members (diagonals or battens) should be analyzed for the action of the member forces (axial, shear and bending) following the design criteria recommended by AISC (Ref 1).

Crane Rails and Joints (5.16)

The project specification must detail acceptable stock lengths, composition, hardness, and tolerances for crane rails to effectively manage joint quantities Utilizing heat-treated rails can significantly enhance their lifespan "Tight fit" bolted splices require round holes in both the rail and splice bar, along with round shank bolts to eliminate gaps upon tightening However, improper maintenance of these splices can lead to looseness, resulting in high-impact forces that may damage the runway and crane For Building Classes A and B, crane rails should be continuously joined using approved welding methods such as puddle arc or thermite to mitigate impact forces from crane wheels Additionally, the specification should outline the approved welding procedures and consider factors like crane loads, side guide rollers, floating rails, thermal expansion, and runway length when selecting rail attachment methods and spacing.

Elastomeric pads, when installed continuously beneath crane rails, effectively minimize fatigue, vibration, impact forces, and noise levels Additionally, it's essential to conduct finished profile grinding prior to securing the crane rail in its final position.

Mains, Ducts and Pipes (3.7.5)

In the design of duct systems and their supports, consideration should be given to but not limited to:

• Potential explosive limits of the conveyed gases

• Duct collapse due to negative pressures

• Differential expansion between inner and outer shells of water-cooled ducts

• Radiation of heat from air-cooled ducts

• Contraction and expansion of steam lines

Investigating refractory mains, ducts, or pipes that experience water-cooled gas flows is essential to identify potential arching effects caused by temperature differences between upper and lower supports.

Ducts transporting saturated gases or gases containing entrained water must be inclined toward an appropriate drain pocket It is essential to consider the characteristics of the dust load in the gas when determining the slope.

Consideration should be given to an accidental full dust loading of any duct due to unusual operating proce- dures or processes.

Table 7.1 Equivalent Length Factor,K L for Lower Segment of Stepped Columns Column ABC Hinged at A and Hinged at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2 = 0.00 1.00 0.91 0.83 0.80 ~0.79 0.78 0.77 0.76 ~0.75 0.74 0.74 0.73 ~0.73 0.73 0.73 0.73 2.00 0.91 0.84 0.80 ~0.79 0.79 0.78 0.78 ~0.78 0.78 0.78 0.79 ~0.79 0.81 0.91 0.94 3.00 0.91 0.84 0.81 ~0.80 0.80 0.80 0.80 ~0.81 0.82 0.84 0.85 ~0.87 0.89 0.91 0.94 5.00 0.91 0.84 0.82 ~0.82 0.83 0.84 0.86 ~0.890 0.92 0.95 0.98 ~1.02 1.06 1.09 1.13 10.00 0.91 0.85 0.87 0.90 0.94 0.99 1.04 1.10 1.16 1.22 1.28 1.34 1.40 1.45 1.51 20.00 0.91 0.88 1.03 1.11 1.20 1.29 1.38 1.47 1.56 1.65 1.74 1.83 1.92 2.00 2.08 40.00 0.91 1.01 1.36 1.50 1.63 1.76 1.90 2.03 2.16 2.29 2.42 2.55 2.67 2.79 2.90 70.00 0.91 1.26 1.77 1.95 2.12 2.30 2.48 2.65 2.83 3.01 3.18 3.34 3.51 3.67 3.82 100.00 0.91 1.49 2.10 2.31 2.52 2.74 2.95 3.16 3.37 3.58 3.79 3.99 4.19 4.37 4.56 P 1 /P 2 = 0.10 1.00 0.92 0.85 0.81 ~0.80 0.79 0.79 0.78 ~0.77 0.77 0.76 0.76 ~0.76 0.76 0.75 0.75 2.00 0.92 0.85 0.82 ~0.81 0.81 0.81 0.81 ~0.81 0.81 0.82 0.83 ~0.84 0.85 0.86 0.87 3.00 0.92 0.85 0.83 ~0.83 0.83 0.83 0.84 ~0.85 0.87 0.88 0.90 ~0.92 0.95 0.97 0.99 5.00 0.92 0.86 0.85 ~0.86 0.87 0.90 0.92 ~0.95 0.99 1.02 1.06 ~1.09 1.13 1.16 1.20 10.00 0.92 0.88 0.94 0.98 1.03 1.09 1.151 1.21 1.27 1.33 1.39 1.45 1.51 1.57 1.62 20.00 0.92 0.95 1.17 1.26 1.35 1.44 1.54 1.63 1.72 1.81 1.90 1.99 2.08 2.16 2.24 40.00 0.92 1.19 1.58 1.71 1.85 1.99 2.12 2.26 2.39 2.52 2.65 2.77 2.90 3.02 3.13 70.00 0.93 1.52 2.05 2.23 2.42 2.60 2.78 2.96 3.13 3.31 3.48 3.65 3.81 3.97 4.12 100.00 0.95 1.80 2.44 2.66 2.87 3.09 3.31 3.52 3.74 3.94 4.15 4.35 4.54 4.73 4.92 P 1 /P 2 = 0.20 1.00 0.92 0.85 0.81 ~0.80 0.79 0.79 0.78 ~0.77 0.77 0.76 0.76 ~0.76 0.76 0.75 0.75 2.00 0.92 0.85 0.82 ~0.81 0.81 0.81 0.81 ~0.81 0.81 0.82 0.83 ~0.84 0.85 0.86 0.87 3.00 0.92 0.85 0.83 ~0.83 0.83 0.83 0.84 ~0.85 0.87 0.88 0.90 ~0.92 0.95 0.97 0.99 5.00 0.92 0.86 0.85 ~0.86 0.87 0.90 0.92 ~0.95 0.99 1.02 1.06 ~1.09 1.13 1.16 1.20 10.00 0.92 0.88 0.94 0.98 1.03 1.09 1.151 1.21 1.27 1.33 1.39 1.45 1.51 1.57 1.62 20.00 0.92 0.95 1.17 1.26 1.35 1.44 1.54 1.63 1.72 1.81 1.90 1.99 2.08 2.16 2.24 40.00 0.92 1.19 1.58 1.71 1.85 1.99 2.12 2.26 2.39 2.52 2.65 2.77 2.90 3.02 3.13 70.00 0.93 1.52 2.05 2.23 2.42 2.60 2.78 2.96 3.13 3.31 3.48 3.65 3.81 3.97 4.12 100.00 0.95 1.80 2.44 2.66 2.87 3.09 3.31 3.52 3.74 3.94 4.15 4.35 4.54 4.73 4.92

Table 7.1 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 2 Column ABC Hinged at A and Hinged at C 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.30 1.000.930.870.84~0.830.820.820.81~0.810.800.800.73~0.800.790.790.79 2.000.930.870.85~0.880.850.850.85~0.860.870.880.79~0.900.910.920.94 3.000.930.880.87~0.870.880.890.90~0.920.940.980.85~1.001.031.051.07 5.000.930.890.91~0.930.950.981.02~1.051.091.160.98~1.201.241.271.31 10.000.930.931.051.111.171.231.301.361.421.551.281.611.671.721.78 20.000.941.091.361.461.561.661.751.851.942.131.742.222.302.392.47 40.000.951.441.862.012.152.292.432.572.702.972.423.103.223.343.46 70.001.001.862.432.622.813.003.193.383.553.733.914.074.244.404.56 100.001.112.202.893.123.353.583.804.024.244.454.664.865.065.255.44 P 1 /P 2= 0.40 1.000.930.880.85~0.840.840.830.83~0.820.820.810.81~0.810.810.810.81 2.000.930.880.87~0.860.860.870.87~0.880.890.900.91~0.920.930.950.96 3.000.930.890.89~0.890.900.910.93~0.940.960.991.01~1.031.051.081.10 5.000.940.900.93~0.960.981.021.05~1.091.131.161.20~1.241.281.311.35 10.000.940.961.101.161.221.291.351.421.481.541.611.671.731.781.84 20.000.941.151.431.531.631.731.831.932.032.122.212.302.392.472.55 40.000.971.521.962.112.262.402.542.682.822.953.093.223.343.463.58 70.001.051.972.562.762.953.153.333.533.713.894.064.234.404.564.72 100.001.192.343.053.293.523.753.984.204.424.634.855.055.255.445.63 P 1 /P 2 = 0.50 1.000.940.890.86~0.850.850.840.84~0.830.830.830.83~0.820.820.820.82 2.000.940.890.88~0.880.880.880.89~0.890.900.920.93~0.940.950.970.98 3.000.940.900.90~0.910.920.930.95~0.970.991.011.03~1.061.081.101.13 5.000.940.920.96~0.981.011.041.08~1.121.161.201.24~1.281.311.351.39 10.000.940.991.141.201.271.331.401.461.531.591.661.721.781.831.89 20.000.951.191.491.591.701.801.902.002.092.192.282.372.462.552.63 40.000.981.592.052.202.342.492.642.782.923.053.193.323.443.573.68 70.001.102.072.682.883.073.273.463.653.844.024.204.374.534.694.86 100.001.252.463.183.423.663.894.124.354.574.795.015.215.415.615.80

Table 7.1 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 3 Column ABC Hinged at A and Hinged at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.60 1.000.940.890.87~0.860.860.850.85~0.840.840.840.84~0.840.830.830.83 2.000.940.900.89~0.890.890.900.90~0.910.920.930.94~0.960.970.981.00 3.000.940.910.91~0.920.930.950.97~0.991.011.031.05~1.081.101.131.15 5.000.940.930.98~1.001.041.071.11~1.151.191.231.27~1.301.341.381.42 10.000.951.011.171.241.301.371.441.501.571.631.701.761.821.881.93 20.000.961.241.541.651.751.851.962.062.152.252.342.432.522.612.69 40.001.001.652.122.272.422.572.722.863.003.143.273.403.533.653.77 70.001.142.152.772.973.173.373.563.763.944.134.314.484.654.824.97 100.001.312.553.303.543.784.024.254.484.704.925.145.345.555.755.93 P 1 /P 2 = 0.70 1.000.950.900.88~0.870.870.860.86~0.850.850.850.85~0.850.850.850.84 2.000.950.910.90~0.900.900.910.91~0.920.930.950.96~0.970.991.001.01 3.000.950.920.93~0.940.950.960.98~1.001.031.051.07~1.101.121.151.17 5.000.950.940.99~1.021.061.091.13~1.171.211.251.29~1.331.371.411.44 10.000.951.031.201.271.331.401.471.541.601.671.731.801.861.911.97 20.000.971.271.581.691.801.902.002.102.202.302.392.492.572.662.74 40.001.021.712.182.332.492.642.782.933.073.213.353.483.613.733.85 70.001.172.222.853.063.263.463.663.854.044.234.404.584.754.925.07 100.001.362.643.393.643.884.124.364.594.825.045.255.465.675.876.05 P 1 /P 2= 0.80 1.000.950.900.88~0.880.870.870.86~0.860.860.860.86~0.850.850.850.85 2.000.950.910.91~0.910.910.920.93~0.940.950.960.97~0.981.001.011.03 3.000.950.920.94~0.950.960.981.00~1.021.041.071.09~1.111.141.161.19 5.000.950.951.01~1.041.071.111.15~1.191.231.271.31~1.651.391.431.47 10.000.961.051.231.291.361.431.501.571.631.701.771.831.891.952.00 20.000.971.301.621.731.841.942.042.152.252.342.442.532.622.712.79 40.001.031.752.232.392.542.692.842.993.133.273.413.543.673.793.91 70.001.212.282.923.133.333.543.743.934.124.314.494.664.835.015.16 100.001.402.703.473.723.974.214.454.694.915.145.355.575.775.976.16

Table 7.1 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 4 Column ABC Hinged at A and Hinged at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.90 1.000.950.910.89~0.880.880.880.87~0.870.870.860.86~0.860.860.860.86 2.000.950.920.91~0.920.920.930.94~0.950.960.970.98~1.001.011.021.04 3.000.950.930.95~0.960.970.991.01~1.031.061.081.10~1.131.151.181.20 5.000.950.961.02~1.051.091.131.17~1.211.251.291.33~1.371.411.451.48 10.000.961.061.251.321.391.461.531.601.661.731.791.861.921.982.03 20.000.981.331.661.761.871.982.082.182.292.382.482.572.662.752.83 40.001.051.792.282.432.592.752.903.043.193.333.473.603.733.853.97 70.001.242.332.983.193.403.603.804.004.194.384.564.744.925.085.24 100.001.432.763.543.804.054.304.534.775.005.225.445.665.876.066.25 P 1 /P 2= 1.00 1.000.950.910.89~0.890.890.880.88~0.880.870.870.87~0.870.870.870.87 2.000.950.920.92~0.920.930.940.95~0.950.970.980.99~1.011.021.041.05 3.000.960.940.96~0.970.981.001.02~1.041.071.091.12~1.141.171.191.22 5.000.960.971.04~1.071.111.141.18~1.231.271.311.35~1.391.431.471.50 10.000.961.081.271.341.411.481.551.621.691.751.821.881.942.002.06 20.000.991.351.681.791.902.012.112.222.322.422.512.612.702.782.87 40.001.061.832.322.482.632.792.943.093.343.383.523.653.783.914.03 70.001.262.383.033.253.453.663.874.064.264.454.634.814.985.155.31 100.001.472.823.613.864.114.364.614.845.075.315.525.735.956.156.34 P 1 /P 2= 2.00 1.000.970.940.93~0.930.920.920.92~0.920.920.920.92~0.910.910.910.91 2.000.970.960.97~0.970.980.991.00~1.011.031.041.06~1.071.091.101.12 3.000.970.981.01~1.031.051.071.10~1.121.141.171.20~1.221.251.281.30 5.000.981.021.11~1.151.191.241.28~1.331.371.411.45~1.501.541.581.61 10.000.991.171.391.461.541.611.691.761.831.901.972.032.102.162.22 20.001.021.501.861.972.092.202.312.422.532.632.732.822.923.003.09 40.001.152.032.562.732.893.063.223.373.533.673.823.964.094.224.34 70.001.422.653.353.583.804.024.234.444.644.845.035.225.405.575.73 100.001.663.143.994.264.534.795.055.295.545.776.006.236.446.646.84

Table 7.2 Equivalent Length Factor,K L for Lower Segment of Stepped Columns Column ABC Rotation Restr ained b ut P er mitted to Sw a y at T op A and Fix ed at Base C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.00 1.001.000.980.96~0.950.930.920.91~0.900.880.870.85~0.830.810.790.77 2.001.081.101.08~1.071.061.041.03~1.010.990.970.95~0.930.910.880.86 3.001.151.181.16~1.141.131.111.09~1.071.051.031.00~0.980.950.920.89 5.001.261.281.25~1.231.211.191.16~1.141.111.081.05~1.020.990.960.93 10.001.421.401.341.321.291.261.231.201.171.131.101.071.031.000.96 20.001.561.491.401.371.341.311.271.241.201.171.131.091.061.020.98 40.001.661.541.441.401.371.331.301.261.221.181.141.111.071.030.99 70.001.721.561.461.421.381.341.311.271.231.191.151.111.071.030.99 100.001.741.571.461.431.391.351.311.271.231.191.151.111.071.041.00 P 1 /P 2= 0.10 1.001.000.980.96~0.950.940.930.92~0.900.890.880.86~0.850.830.810.79 2.001.081.101.09~1.081.071.051.04~1.021.010.990.97~0.950.920.900.88 3.001.151.191.16~1.151.141.121.11~1.091.071.041.02~1.000.970.950.92 5.001.261.291.26~1.241.221.201.18~1.151.131.101.08~1.051.020.990.96 10.001.421.411.351.331.301.281.251.221.191.161.131.091.061.031.00 20.001.561.501.421.391.361.331.291.261.231.191.161.121.091.061.02 40.001.671.551.461.421.391.351.321.281.251.221.181.151.121.101.08 70.001.721.581.471.441.401.371.331.301.271.241.221.221.231.261.30 100.001.741.591.481.451.411.381.351.321.301.301.331.371.421.481.53 P 1 /P 2= 0.20 1.001.000.980.96~0.950.940.930.92~0.910.900.890.87~0.860.840.820.81 2.001.081.111.09~1.081.071.061.05~1.031.021.000.98~0.960.940.920.90 3.001.151.191.17~1.161.151.131.12~1.101.081.061.04~1.010.990.970.94 5.001.261.301.27~1.251.231.211.19~1.171.151.121.10~1.071.041.010.99 10.001.421.421.371.341.321.291.271.241.211.181.151.121.091.061.03 20.001.571.511.431.401.371.341.311.281.251.221.191.171.141.121.10 40.001.671.561.471.441.411.381.351.321.301.281.271.271.291.321.35 70.001.731.591.491.461.441.411.391.391.411.451.501.551.611.681.74 100.001.751.601.511.481.471.471.491.541.611.681.751.831.911.992.07

Table 7.2 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 2 Column ABC Rotation Restr ained b ut P er mitted to Sw a y at T op A and Fix ed at Base C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.30 1.001.000.980.96~0.960.950.940.93~0.920.910.890.88~0.870.850.830.82 2.001.081.111.10~1.091.081.071.06~1.041.031.010.99~0.980.960.940.92 3.001.151.191.18~1.171.161.141.13~1.111.091.071.05~1.031.010.990.96 5.001.261.301.27~1.261.241.221.20~1.181.161.141.11~1.091.061.041.01 10.001.431.431.381.351.331.311.281.261.231.201.181.151.121.101.08 20.001.571.521.441.421.391.361.331.311.281.261.231.221.211.211.21 40.001.671.571.491.461.431.411.391.371.361.371.401.431.481.531.58 70.001.731.601.521.501.481.481.501.551.611.671.741.821.891.972.05 100.001.751.621.551.551.571.631.701.791.871.962.062.152.242.342.43 P 1 /P 2= 0.40 1.001.000.980.97~0.960.950.940.93~0.920.910.90.89~0.870.860.850.83 2.001.081.110.10~1.091.091.071.06~1.051.041.021.01~0.990.970.950.93 3.001.161.201.18~1.171.161.151.14~1.121.101.091.07~1.051.031.000.98 5.001.271.311.28~1.271.251.231.21~1.191.171.151.13~1.111.081.061.04 10.001.431.431.381.361.341.321.301.271.251.221.201.181.151.141.12 20.001.571.521.451.431.401.381.351.331.311.291.281.281.281.291.32 40.001.681.581.501.481.461.441.431.431.451.481.521.571.631.691.75 70.001.731.611.541.541.541.571.631.691.771.851.932.022.102.192.27 100.001.761.631.601.641.701.791.881.982.082.182.282.392.492.602.70 P 1 /P 2= 0.50 1.001.000.980.97~0.960.950.950.94~0.930.920.910.89~0.880.870.850.84 2.001.081.111.10~1.101.091.081.07~1.061.041.031.02~1.000.980.960.95 3.001.161.201.19~1.181.171.161.14~1.131.111.101.08~1.061.041.021.00 5.001.271.311.29~1.271.261.241.22~1.211.191.171.14~1.121.101.081.06 10.001.431.441.391.371.351.331.311.291.261.241.221.201.191.171.16 20.001.581.531.461.441.421.391.371.351.341.331.331.331.351.381.41 40.001.681.591.521.501.481.471.481.491.531.581.631.691.751.821.89 70.001.741.621.571.581.611.671.741.821.901.992.082.182.272.362.46 100.001.761.641.671.731.821.922.022.132.242.352.472.582.692.812.92

Table 7.2 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 3 Column ABC Rotation Restr ained b ut P er mitted to Sw a y at T op A and Fix ed at Base C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.60 1.001.000.990.97~0.960.960.950.94~0.930.920.910.9~0.890.880.860.85 2.001.081.111.11~1.101.091.091.08~1.061.051.041.02~1.010.990.980.96 3.001.161.201.19~1.181.181.161.15~1.141.121.111.09~1.071.051.031.02 5.001.271.311.29~1.281.271.251.23~1.221.201.181.16~1.141.121.101.08 10.001.431.441.401.381.361.341.321.301.281.261.241.231.211.211.20 20.001.581.541.471.451.431.411.391.381.371.361.371.391.411.441.48 40.001.681.601.531.521.511.511.521.561.601.661.721.791.861.932.00 70.001.741.631.611.631.681.751.831.922.012.112.212.312.402.502.60 100.001.761.661.731.821.922.032.142.262.382.52.612.732.852.973.10 P 1 /P 2= 0.70 1.001.000.990.97~0.970.960.950.94~0.940.930.920.91~0.890.880.870.86 2.001.081.121.11~1.111.101.091.08~1.071.061.051.03~1.021.000.990.97 3.001.161.201.20~1.191.181.171.16~1.141.131.111.10~1.081.061.051.03 5.001.271.321.30~1.291.271.261.24~1.221.211.191.17~1.151.131.121.10 10.001.431.451.411.391.371.351.331.311.291.281.261.251.241.241.24 20.001.581.541.481.461.441.421.411.401.391.401.411.441.471.501.55 40.001.691.601.541.531.531.541.571.611.671.731.81.871.942.022.09 70.001.741.641.641.681.741.821.912.012.112.212.312.412.522.622.73 100.001.771.681.801.892.002.122.242.362.492.612.742.862.993.123.24 P 1 /P 2= 0.80 1.001.000.990.97~0.970.960.950.95~0.940.930.920.91~0.900.890.880.86 2.001.091.121.11~1.111.101.091.09~1.081.061.051.04~1.031.011.000.98 3.001.161.211.20~1.191.181.171.16~1.151.141.121.11~1.091.081.061.04 5.001.271.321.30~1.291.281.261.25~1.231.221.201.18~1.161.151.131.12 10.001.431.451.411.391.381.361.341.321.311.291.281.271.271.271.27 20.001.581.551.491.471.451.441.431.421.421.431.451.481.521.561.60 40.001.691.611.561.551.561.581.611.661.721.791.861.942.012.092.17 70.001.741.651.671.721.801.891.982.082.192.292.402.512.622.722.83 100.001.771.691.851.962.082.202.332.462.582.712.842.983.113.243.37

Table 7.2 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 4 Column ABC Rotation Restr ained b ut P er mitted to Sw a y at T op A and Fix ed at Base C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.90 1.001.000.990.97~0.970.960.960.95~0.940.930.920.91~0.900.890.880.87 2.001.091.121.12~1.111.111.101.09~1.081.071.061.05~1.031.021.010.99 3.001.161.211.20~1.201.191.181.17~1.161.141.131.11~1.101.081.071.06 5.001.271.321.30~1.291.281.271.25~1.241.221.211.19~1.181.161.151.14 10.001.441.451.421.41.381.371.351.331.321.31.291.291.291.291.3 20.001.581.551.501.481.461.451.441.441.441.461.481.521.561.61.65 40.001.691.611.571.571.581.611.651.711.771.841.922.002.082.162.24 70.001.751.661.701.761.851.942.042.152.262.372.482.592.72.812.92 100.001.771.711.902.022.142.272.42.532.672.82.943.073.213.343.48 P 1 /P 2= 1.00 1.001.000.990.98~0.970.970.960.95~0.940.940.930.92~0.910.90.890.88 2.001.091.121.12~1.111.111.11.09~1.081.071.061.05~1.041.031.011.00 3.001.161.211.21~1.201.191.181.17~1.161.151.141.12~1.111.091.081.07 5.001.271.321.31~1.301.291.271.26~1.251.231.221.20~1.191.171.161.15 10.001.441.461.421.411.391.371.361.341.331.321.311.311.311.321.33 20.001.581.551.501.491.471.461.461.461.471.491.521.551.61.641.69 40.001.691.621.581.581.61.641.681.751.821.891.972.052.132.222.3 70.001.751.671.731.81.891.992.12.212.322.432.542.662.772.893.00 100.001.771.721.952.072.22.332.472.62.742.883.023.163.293.433.57 P 1 /P 2= 2.00 1.001.000.990.98~0.980.980.970.97~0.960.960.950.94~0.940.930.920.92 2.001.091.131.13~1.131.131.121.12~1.111.111.11.09~1.081.071.071.06 3.001.161.221.22~1.221.221.211.2~1.201.191.181.17~1.161.151.141.14 5.001.271.341.33~1.331.321.311.3~1.291.281.271.26~1.261.251.251.25 10.001.441.481.451.441.431.421.411.411.41.411.411.421.441.471.49 20.001.591.581.551.541.541.541.561.581.621.661.711.761.821.881.94 40.001.701.661.671.711.761.821.91.992.082.172.262.632.462.562.66 70.001.761.741.932.042.162.282.412.542.672.82.933.073.203.333.47 100.001.791.852.222.372.532.682.8433.163.323.483.643.803.964.13

Table 7.3 Equivalent Length Factor,K L for Lower Segment of Stepped Columns Column ABC Hinged at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.00 1.000.610.530.50~0.490.480.470.47~0.460.460.460.46~0.460.460.460.46 2.000.610.530.50~0.490.490.490.49~0.490.500.510.52~0.520.530.530.54 3.000.610.530.50~0.500.500.510.52~0.540.550.560.57~0.580.590.590.60 5.000.610.530.52~0.530.550.580.60~0.620.640.650.66~0.670.680.680.68 10.000.610.640.620.660.690.720.740.760.780.790.800.800.800.800.79 20.000.610.630.780.820.860.890.910.920.930.930.920.920.910.890.87 40.000.610.810.971.001.031.041.051.051.051.041.001.000.980.960.93 70.000.610.971.111.131.151.151.141.131.121.101.071.051.020.990.96 100.000.621.081.191.201.211.201.191.171.151.121.101.071.041.000.97 P 1 /P 2= 0.10 1.000.610.550.52~0.510.500.490.49~0.490.480.480.48~0.480.480.480.48 2.000.610.550.52~0.520.520.520.52~0.530.540.550.55~0.560.570.570.57 3.000.610.550.53~0.530.540.560.57~0.580.600.610.62~0.630.630.640.64 5.000.610.550.57~0.590.620.640.66~0.680.700.710.72~0.730.730.730.73 10.000.610.580.700.740.770.800.830.840.860.870.870.870.870.860.85 20.000.610.740.900.930.970.991.011.021.021.021.011.000.990.970.95 40.000.610.961.111.141.161.171.171.171.161.141.121.101.081.051.02 70.000.651.161.281.291.291.291.281.261.241.221.191.161.161.101.08 100.000.751.281.371.371.371.351.331.311.281.251.231.201.181.161.16 P 1 /P 2= 0.20 1.000.620.560.53~0.520.520.510.51~0.500.500.500.50~0.500.500.500.50 2.000.620.560.54~0.540.540.540.55~0.560.570.580.58~0.590.590.600.60 3.000.620.560.56~0.560.580.590.61~0.620.630.650.66~0.660.670.670.67 5.000.620.570.61~0.640.660.690.71~0.730.740.760.77~0.770.780.780.77 10.000.620.640.770.810.840.870.890.910.920.930.930.930.930.920.91 20.000.620.820.981.021.051.071.091.101.101.091.091.071.061.041.02 40.000.631.071.221.251.261.271.271.261.251.231.211.191.171.151.13 70.000.761.291.401.411.411.411.391.371.351.331.311.291.281.281.30 100.000.891.431.511.511.501.481.461.441.421.401.391.421.421.451.49

Table 7.3 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 2 Column ABC Hinged at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.30 1.000.620.570.54~0.530.530.530.52~0.520.520.520.52~0.520.520.520.52 2.000.620.570.56~0.560.560.570.58~0.580.590.600.61~0.610.620.620.62 3.000.620.580.58~0.590.610.620.64~0.650.660.680.69~0.690.700.700.70 5.000.630.590.65~0.680.700.730.75~0.770.780.790.80~0.810.810.810.81 10.000.630.690.820.860.890.920.940.960.970.980.980.980.970.970.95 20.000.630.891.051.091.121.141.151.161.161.161.151.141.121.101.08 40.000.681.161.311.331.351.351.351.341.331.311.291.281.261.251.24 70.000.841.401.511.511.511.501.491.471.451.441.431.431.441.461.49 100.000.991.551.621.621.601.591.571.551.551.551.561.591.641.691.74 P 1 /P 2= 0.40 1.000.630.580.55~0.550.540.540.54~0.530.530.530.53~0.530.530.530.53 2.000.630.580.57~0.570.580.590.60~0.600.610.620.63~0.630.640.640.64 3.000.630.590.60~0.610.630.650.66~0.680.690.700.71~0.720.720.730.73 5.000.630.610.68~0.710.730.760.78~0.800.810.830.84~0.840.850.850.84 10.000.630.730.860.900.930.960.981.001.011.021.021.021.011.011.00 20.000.640.941.111.141.171.191.211.211.211.211.201.191.171.161.14 40.000.721.231.381.401.411.421.421.411.391.381.361.351.341.341.34 70.000.911.481.591.591.591.581.571.551.541.531.531.551.571.611.65 100.001.071.651.711.711.691.681.661.661.661.681.711.751.811.871.93 P 1 /P 2= 0.50 1.000.630.580.56~0.560.550.550.55~0.550.540.540.54~0.540.540.540.54 2.000.630.590.59~0.590.600.600.61~0.620.630.640.65~0.650.660.660.66 3.000.630.600.62~0.630.650.670.68~0.700.710.720.73~0.740.750.750.75 5.000.640.630.71~0.730.760.780.81~0.820.840.850.86~0.870.870.870.87 10.000.640.760.900.940.971.001.021.031.051.051.061.051.051.041.03 20.000.650.991.151.191.221.241.251.261.261.251.241.231.221.211.19 40.000.761.281.441.461.471.481.471.461.451.441.421.411.411.421.43 70.000.971.551.661.661.661.651.641.621.611.611.621.651.681.721.77 100.001.131.731.791.791.771.761.751.751.761.791.831.881.952.012.08

Table 7.3 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 3 Column ABC Hinged at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.60 1.000.640.590.57~0.570.560.560.56~0.560.560.550.55~0.550.550.550.55 2.000.640.600.60~0.600.610.620.63~0.640.650.650.66~0.670.670.680.68 3.000.640.610.64~0.650.670.680.70~0.720.730.740.75~0.760.760.770.77 5.000.640.650.73~0.760.780.810.83~0.850.860.880.89~0.890.890.890.89 10.000.640.790.930.971.001.031.051.061.081.081.091.081.081.071.06 20.000.671.021.191.231.261.281.291.301.301.291.281.271.261.251.24 40.000.801.331.481.511.521.521.521.511.501.491.481.471.471.481.50 70.001.011.611.721.721.721.711.691.681.681.691.701.731.771.821.88 100.001.181.791.851.851.831.821.821.821.851.881.931.992.062.132.21 P 1 /P 2= 0.70 1.000.640.600.58~0.570.570.570.57~0.560.560.560.56~0.560.560.560.56 2.000.640.610.61~0.610.620.630.64~0.650.660.670.67~0.680.690.690.69 3.000.640.620.65~0.670.680.700.72~0.730.750.760.77~0.770.780.780.78 5.000.640.660.75~0.780.800.830.85~0.870.880.900.90~0.910.910.910.91 10.000.650.810.950.991.021.051.071.091.101.111.111.111.111.101.09 20.000.681.061.221.261.291.311.321.331.331.321.321.311.291.281.28 40.000.831.381.531.551.561.571.561.551.541.531.521.521.531.541.57 70.001.051.661.771.771.771.761.751.741.741.751.771.811.851.911.96 100.001.231.851.911.901.891.881.881.891.921.962.022.082.152.232.31 P 1 /P 2= 0.80 1.000.610.600.58~0.580.580.580.57~0.570.570.570.57~0.570.570.570.57 2.000.640.610.62~0.620.630.640.65~0.660.670.680.69~0.690.700.700.70 3.000.650.630.66~.0680.700.710.73~0.750.760.770.78~0.790.790.800.80 5.000.650.680.76~0.790.820.840.87~0.880.900.910.92~0.930.930.930.93 10.000.660.830.971.011.051.071.101.111.121.131.131.131.131.121.11 20.000.691.081.251.291.321.341.351.361.361.351.341.341.331.321.31 40.000.851.411.561.591.601.601.601.591.581.571.571.571.571.591.62 70.001.081.711.811.811.811.801.791.791.791.801.831.871.921.982.04 100.001.271.901.961.951.941.931.931.951.982.032.092.162.242.322.40

Table 7.3 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 4 Column ABC Hinged at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.90 1.000.650.610.59~0.590.580.580.58~0.580.580.580.58~0.580.580.580.58 2.000.650.620.63~0.630.640.650.66~0.670.680.690.70~0.700.710.710.71 3.000.650.640.67~0.690.710.730.74~0.760.770.780.79~0.800.810.810.81 5.000.650.690.78~0.810.830.860.88~0.900.920.930.94~0.940.950.950.95 10.000.660.850.991.031.071.091.121.131.141.151.151.151.151.141.13 20.000.701.111.281.321.341.361.381.381.381.381.371.361.351.351.34 40.000.881.441.601.621.631.631.631.621.611.611.601.601.621.641.67 70.001.111.751.851.851.851.841.831.831.831.851.881.931.982.042.10 100.001.301.942.001.991.981.981.982.002.042.092.162.232.312.392.47 P 1 /P 2= 1.00 1.000.650.610.60~0.590.590.590.59~0.590.590.590.59~0.590.590.590.58 2.000.650.630.63~0.640.650.660.67~0.680.690.700.71~0.710.720.720.72 3.000.650.640.68~0.700.720.740.75~0.770.780.790.80~0.810.820.820.82 5.000.650.700.79~0.820.850.870.89~0.910.930.940.95~0.960.960.960.96 10.000.660.861.011.051.081.111.131.151.161.171.171.171.171.161.15 20.000.711.161.301.341.371.391.401.401.401.401.391.391.381.371.37 40.000.901.471.621.651.661.661.661.651.641.641.631.641.651.681.71 70.001.141.781.881.881.881.871.871.861.871.891.931.972.032.092.16 100.001.331.982.032.032.022.022.032.052.092.142.212.292.372.452.54 P 1 /P 2= 2.00 1.000.670.640.63~0.630.630.630.63~0.630.630.630.63~0.630.630.620.62 2.000.670.660.68~0.690.700.710.72~0.730.740.750.76~0.770.770.780.78 3.000.670.690.74~0.760.780.800.82~0.830.850.860.87~0.880.880.890.89 5.000.680.770.87~0.900.930.950.98~1.001.011.021.03~1.041.041.051.05 10.000.700.961.111.151.191.221.241.261.271.281.281.281.281.271.27 20.000.781.251.441.471.501.521.541.541.541.541.531.531.531.531.53 40.001.011.641.791.821.831.831.831.821.821.821.831.851.881.911.96 70.001.291.982.082.092.082.082.082.092.112.152.202.262.332.412.49 100.001.502.202.262.252.252.262.282.322.382.462.542.632.732.832.93

Table 7.4 Equivalent Length Factor,K L for Lower Segment of Stepped Columns Column ABC Fix ed at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.00 1.000.490.470.45~0.440.430.420.41~0.400.400.390.38~0.370.370.370.36 2.000.520.490.47~0.460.450.440.43~0.420.410.400.40~0.400.400.410.42 3.000.540.510.47~0.460.450.440.43~0.420.420.420.43~0.440.450.460.47 5.000.560.520.48~0.470.460.450.44~0.440.460.480.49~0.410.520.540.54 10.000.580.530.490.470.470.500.530.560.580.600.620.640.650.660.67 20.000.600.530.530.570.610.650.680.710.730.750.770.780.780.780.78 40.000.610.550.690.740.780.820.850.870.890.900.900.900.890.880.87 70.000.610.660.840.890.930.960.980.991.001.000.990.980.960.940.92 100.000.610.750.940.981.011.041.051.061.051.041.031.010.990.970.94 P 1 /P 2= 0.10 1.000.490.470.45~0.440.430.430.42~0.410.400.400.39~0.380.380.380.38 2.000.520.500.47~0.460.450.440.43~0.430.420.420.42~0.420.420.430.44 3.000.540.510.48~0.470.460.450.44~0.440.440.440.45~0.460.470.480.49 5.000.560.520.49~0.480.470.460.46~0.480.490.510.53~0.540.560.570.58 10.000.590.530.490.490.520.550.580.600.630.650.670.690.700.700.71 20.000.600.540.590.640.680.710.740.770.800.810.830.840.840.940.83 40.000.610.610.780.830.870.900.930.950.970.970.970.970.960.940.93 70.000.610.760.951.001.031.061.071.081.081.081.071.051.031.010.98 100.000.620.881.071.101.131.151.161.151.151.131.121.091.071.041.01 P 1 /P 2= 0.20 1.000.500.470.45~0.450.440.430.42~0.420.410.400.40~0.390.390.390.39 2.000.520.500.48~0.470.460.450.44~0.430.430.430.43~0.430.440.450.45 3.000.540.510.48~0.470.470.460.45~0.450.450.460.47~0.480.490.500.51 5.000.570.520.49~0.480.480.480.49~0.500.520.540.56~0.570.590.600.60 10.000.590.530.510.530.560.590.620.640.670.690.710.720.730.740.74 20.000.600.540.640.690.730.760.800.820.850.860.870.880.880.880.87 40.000.610.670.850.900.940.971.001.021.031.031.031.031.011.000.98 70.000.610.851.041.081.111.141.151.161.161.151.141.121.091.071.05 100.000.620.981.161.201.221.241.251.241.221.211.191.171.141.121.10

Table 7.4 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 2 Column ABC Fix ed at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.30 1.000.500.480.46~0.450.440.440.43~0.420.420.410.41~0.300.400.400.40 2.000.530.500.48~0.470.460.450.45~0.440.440.440.44~0.450.450.460.47 3.000.540.520.49~0.480.470.460.46~0.460.470.480.49~0.500.510.520.53 5.000.570.530.50~0.490.490.490.51~0.530.540.560.58~0.590.610.620.63 10.000.590.540.530.560.590.620.650.670.700.720.740.750.760.770.77 20.000.600.550.680.730.770.810.840.860.890.900.910.920.920.920.91 40.000.610.720.900.950.991.021.051.071.081.081.081.071.061.041.02 70.000.620.911.101.151.181.201.211.221.221.211.191.171.151.131.12 100.000.621.051.241.271.291.311.311.301.291.271.251.231.221.221.24 P 1 /P 2= 0.40 1.000.500.480.46~0.450.450.440.43~0.430.420.420.41~0.410.410.410.40 2.000.530.500.48~0.470.470.460.45~0.450.450.450.45~0.460.470.470.48 3.000.550.520.49~0.480.480.470.47~0.470.480.490.50~0.520.530.540.55 5.000.570.530.50~0.500.500.510.53~0.540.560.580.60~0.610.630.640.64 10.000.590.540.550.580.610.640.670.700.730.750.760.780.790.790.80 20.000.610.570.720.760.800.840.870.900.920.940.950.950.950.950.94 40.000.610.760.951.001.041.071.091.111.121.121.121.111.101.081.07 70.000.620.971.161.201.231.251.271.271.261.251.241.221.211.191.20 100.000.621.111.301.331.351.371.371.361.351.331.311.301.301.331.37 P 1 /P 2= 0.50 1.000.500.480.46~0.460.450.440.44~0.430.430.420.42~0.410.410.410.41 2.000.530.510.49~0.480.470.460.46~0.460.460.460.46~0.470.480.480.49 3.000.550.520.50~0.490.480.480.48~0.490.490.510.52~0.530.540.550.56 5.000.570.530.51~0.510.510.520.54~0.560.580.600.61~0.630.640.650.66 10.000.590.550.570.600.630.670.700.720.750.770.780.800.810.810.82 20.000.610.600.750.790.830.870.900.930.950.960.980.980.980.970.97 40.000.620.800.981.031.071.111.131.151.161.161.151.151.131.121.10 70.000.621.011.201.251.281.301.311.311.311.301.281.271.251.251.27 100.000.631.161.351.381.401.411.411.411.391.381.371.371.391.431.47

Table 7.4 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 3 Column ABC Fix ed at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.60 1.000.500.480.46~0.460.450.450.44~0.430.430.430.42~0.420.420.420.42 2.000.530.510.49~0.480.470.470.47~0.460.460.470.47~0.480.490.490.50 3.000.550.520.50~0.490.490.490.49~0.490.500.520.53~0.540.550.560.57 5.000.570.540.51~0.510.520.540.55~0.570.590.610.63~0.640.660.670.67 10.000.590.550.590.620.650.680.710.740.770.790.800.820.830.830.83 20.000.610.620.770.810.860.890.930.950.970.991.001.001.001.000.99 40.000.620.831.021.061.111.141.161.181.191.191.181.181.161.151.14 70.000.621.051.241.291.321.341.351.351.341.331.321.311.301.311.34 100.000.651.211.391.431.451.461.451.451.431.421.411.431.461.511.56 P 1 /P 2= 0.70 1.000.500.480.46~0.460.450.450.44~0.440.430.430.43~0.420.420.420.42 2.000.530.510.49~0.480.480.470.47~0.470.470.470.48~0.490.490.500.51 3.000.550.520.50~0.500.490.490.50~0.500.510.520.54~0.550.560.570.58 5.000.570.540.52~0.520.530.550.57~0.590.600.620.64~0.660.670.680.69 10.000.590.550.600.630.670.700.730.760.780.800.820.830.840.850.85 20.000.610.400.790.840.880.910.950.970.991.011.021.021.021.021.01 40.000.620.851.041.091.131.161.191.211.211.211.211.201.191.181.17 70.000.631.081.281.321.351.371.381.381.371.361.351.341.341.361.39 100.000.681.241.431.461.481.491.491.481.471.461.461.481.521.581.63 P 1 /P 2= 0.80 1.000.500.480.47~0.460.460.450.45~0.440.440.430.43~0.430.430.430.43 2.000.530.510.49~0.490.480.480.47~0.470.480.480.49~0.490.500.510.51 3.000.550.530.51~0.500.500.500.50~0.510.520.530.55~0.560.570.580.59 5.000.570.540.52~0.530.540.560.58~0.600.620.630.65~0.670.680.690.70 10.000.600.560.610.650.680.710.740.770.800.820.830.850.860.860.86 20.000.610.650.810.850.900.930.970.991.011.031.041.041.041.041.03 40.000.620.871.071.121.161.191.211.231.241.241.231.221.211.201.19 70.000.631.111.311.351.381.401.411.411.401.391.381.371.381.401.44 100.000.701.281.461.501.521.521.521.511.501.501.501.531.581.641.70

Table 7.4 Equivalent Length Factor,K L for Lower Segment of Stepped Columns,continued,page 4 Column ABC Fix ed at A and Fix ed at C a r 0.10 0.20 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 B P 1 /P 2= 0.90 1.000.500.480.47~0.460.460.450.45~0.430.440.440.43~0.430.430.430.43 2.000.530.510.49~0.490.480.480.48~0.480.480.490.49~0.500.510.510.52 3.000.550.530.51~0.500.500.500.51~0.520.530.540.55~0.560.580.590.59 5.000.570.540.53~0.530.550.560.58~0.600.630.640.66~0.680.690.700.71 10.000.600.560.620.660.690.730.760.780.810.830.850.860.870.870.88 20.000.610.670.820.870.910.950.981.011.031.041.051.061.061.051.04 40.000.620.891.091.141.181.211.231.251.261.261.251.251.231.221.22 70.000.641.131.331.371.401.421.431.431.431.421.411.401.411.441.49 100.000.721.301.491.531.541.551.551.541.531.531.541.571.631.691.75 P 1 /P 2= 1.00 1.000.500.480.47~0.460.460.450.45~0.450.440.440.44~0.440.440.430.43 2.000.530.510.49~0.490.490.480.48~0.480.490.490.50~0.500.510.520.52 3.000.550.530.51~0.510.510.510.51~0.520.530.550.56~0.570.580.590.60 5.000.570.540.53~0.540.550.570.59~0.610.630.650.67~0.680.700.710.71 10.000.600.570.630.670.700.740.770.790.820.840.860.870.880.880.89 20.000.610.680.840.880.930.961.000.021.041.061.071.071.071.071.06 40.000.620.911.111.151.201.231.251.271.281.281.271.261.251.251.24 70.000.641.151.351.401.431.451.451.461.451.441.431.431.451.481.52 100.000.731.331.521.551.571.581.571.571.561.561.571.611.671.731.80 P 1 /P 2= 2.00 1.000.500.490.48~0.480.470.470.47~0.460.460.460.46~0.460.460.460.46 2.000.530.520.51~0.510.410.410.41~0.510.410.520.53~0.540.540.550.56 3.000.550.540.53~0.530.530.540.55~0.560.570.590.60~0.610.620.630.64 5.000.580.560.56~0.580.600.620.64~0.660.680.700.72~0.730.750.760.76 10.000.600.600.690.730.770.800.830.860.890.910.920.940.950.950.95 20.000.620.750.920.971.011.051.081.111.131.151.151.161.161.151.15 40.000.641.011.211.271.311.341.361.381.381.391.381.381.371.381.39 70.000.711.281.491.531.561.581.591.591.581.581.581.601.641.591.75 100.00.831.471.671.701.721.731.721.721.721.741.781.851.921.992.07

Symbols

Forces, stresses, and moments are measured in kips, kips per square inch (ksi), and kip feet (kip ft), while floor and wind loadings are quantified in kips per square foot (ksf).

The cross-sectional area, measured in square inches, is essential for determining the clear distance between transverse stiffeners in a plate girder Additionally, the ratio of the upper segment length of a crane column to the total length, extending from the lowest roof connection to the footing, plays a crucial role in structural analysis and design.

The B ratio represents the comparison of the maximum moment of inertia of the lower combined crane column section to that of the upper section around the same axis Additionally, the term "b f" refers to the flange width of a rolled beam or plate girder, measured in inches.

The coefficients (C m) used in bending terms of column interaction formulas are essential for accurately accounting for load distribution and end conditions The variable "c c" represents the distance from the neutral axis of the complete lower cross-section of a crane column to the centroid of the crane shaft component, measured in inches Similarly, "c m" indicates the distance from the neutral axis of the lower cross-section to the extreme fiber on the crane side, also measured in inches Finally, "e" denotes the eccentricity, measured in inches, which is critical for understanding the behavior of crane columns under load.

F a Axial stress allowed in the absence of bending moment, ksi

F e Bumper end force at 100% speed, kips

F bx Allowable stress for bending about the (X-X) axis, ksi

F by Allowable stress for bending about the (Y-Y) axis, ksi

F′ ex Equivalent Euler buckling stress of a stepped crane column, divided by factor of safety, ksi

F′ ey Equivalent Euler buckling stress component of lower segment of a crane column, divided by factor of safety, ksi

The specified minimum yield stress of steel, denoted as \( f_y \), is measured in ksi, while the computed average axial stress is represented as \( f_a \) in ksi The average axial stress in the crane column component of a stepped column is referred to as \( f'_{a} \), and the computed bending stress is indicated by \( f_b \) in ksi Additionally, the stresses due to the bending moment about the X-X and Y-Y axes are represented as \( f_{bx} \) and \( f_{by} \), respectively The ultimate compressive strength of concrete at 28 days, unless otherwise specified, is denoted as \( f'_{c} \) in ksi Effective prestress after losses is represented as \( f_{pe} \) in ksi, and shear stress is indicated by \( f_v \) in ksi The acceleration due to gravity is 32.2 fps², while the clear depth of the web between flanges is measured in inches as \( h \), and the depth of the girder between flange centroids is also measured in inches as \( h_f \).

I 0 Moment of inertia, about X-X axis, in 4 (see Fig 7.4)

I S Moment of inertia of a pair of stiffeners about the centerline of the web, in 4

K L Equivalent column length factor for lower shaft

K U Equivalent column length factor for upper shaft k Modulus of subgrade reaction, pcf

L Actual overall length of a member, ft.

P 1 Column load in upper segment of a stepped crane column, kips

P 2 Column load added to lower segment of a stepped crane column including girder reactions, wall, utility loads, etc.

Q Side thrust on crane runway girder, kips

Q (eff) Modified side thrust on crane runway girder, kips

Q t(eff) Modified side thrust on bottom flange of crane runway girder

S B Bumper stroke, in. t w Thickness of beam or girder web, in. t a Thickness of lateral plate in crane runway girder, in. t f Thickness of beam or girder flange, in.

V B Bridge load rated speed, fps

W T Trolley weight, kips w e Effective width of auxiliary plate, in. x,y (As subscripts) axes about which bending takes place, coordinate axes