Structural analysis in theory and practice

[...]... f1 t an br i uil F1 (ii) (iii) Figure 1.10 and: F3 ϭ F1 sin f3 csc f1 or: F1 /sin f1 ϭ F2 /sin f2 ϭ F3 /sin f3 Example 1.2 Determine the angle of inclination and magnitude of the support reaction at end 1 of the pin-jointed truss shown in Figure 1.11 End 1 of the truss has a hinged support, and end 2 has a roller support Structural Analysis: In Theory and Practice 10 F3 ϭ 20 kips 6 3 4 8 ft V2 ϭ 10... shown in Figure S1.4 In addition, determine the forces produced in the members of the crane 3 50 kips 30 ft 1 H1 2 V1 H2 V2 20 ft 10 ft Figure S1.4 Structural Analysis: In Theory and Practice 16 S1.5 Determine the reactions at the supports of the pin-jointed frame shown in Figure S1.5 In addition, determine the force produced in member 13 20 ft 10 kips 2 3 20 ft 1 4 H1 H4 V1 V4 Figure S1.5 S1.6 Determine... body diagrams, the internal forces in the members at the cut line may be obtained The values of the member forces are indicated at (ii) and (iii) Example 1.3 The pin-jointed truss shown in Figure 1.13 has a hinged support at support 1 and a roller support at support 2 Determine the forces in members 15, 35, and 34 caused by the horizontal applied load of 20 kips at joint 3 A Cut line H3 ϭ 20 kips 3... 4 cut line 5.59 kips H1 ϭ 10 kips H1 ϭ 10 kips 1 5 A V1 ϭ 15 kips (i) Applied loads and support reactions 2 12.5 kips V2 ϭ 25 kips V4 ϭ 20 kips V1 ϭ 15 kips (ii) Left hand free body diagram 15 kips 5.59 kips 12.5 kips V2 ϭ 25 kips (iii) Right hand free body diagram Figure 1.12 Structural Analysis: In Theory and Practice 12 loads at joint 3, and the internal forces acting on it from the right-hand portion... are analyzed using the equations of static equilibrium with the following assumptions: ● ● all members are connected at their nodes with frictionless hinges the centroidal axes of all members at a node intersect at one point so as to avoid eccentricities Structural Analysis: In Theory and Practice 20 Bowstring Sawtooth Pratt Howe Warren Fink Figure 2.1 Figure 2.2 ● ● ● all loads, including member weight,... displacements and stresses corresponding to each force applied separately The principle applies to all linear-elastic structures in which displacements are proportional to applied loads and which are constructed from materials with a linear stress-strain relationship This enables loading on a structure to be broken down into simpler components to facilitate analysis As shown in Figure 1.14, a pin-jointed truss... structure Similarly, the right-hand portion of the truss is in equilibrium under the actions of the support reactions of the complete structure at 2, the applied load at joint 4, and the internal forces acting on it from the lefthand portion of the structure The internal forces in the members consist of a compressive force in member 34 and a tensile force in members 45 and 25 By using the three equations of... for determining the internal forces in a structure using the concept of a free body diagram Figure 1.12 (i) shows the applied loads and support reactions acting on the pin-jointed truss that was analyzed in Example 1.1 The structure is cut at section A-A, and the two parts of the truss are separated as shown at (ii) and (iii) to form two free body diagrams The left-hand portion of the truss is in equilibrium... determinacy A statically determinate truss is one in which all member forces and external reactions may be determined by applying the equations of equilibrium In a simple truss, external reactions are provided by either hinge supports or roller supports, as shown in Figure 2.3 (i) and (ii) The roller support provides only one degree of restraint, in the vertical direction, and both horizontal and Statically... n ϩ r ϭ 2j A truss is statically indeterminate, as shown in Figure 2.4, when: n ϩ r Ͼ 2j (i) (ii) Figure 2.4 The truss at (i) is internally redundant, and the truss at (ii) is externally redundant A truss is unstable, as shown in Figure 2.5, when: n ϩ r Ͻ 2j Structural Analysis: In Theory and Practice 22 (i) (ii) Figure 2.5 The truss at (i) is internally deficient, and the truss at (ii) is externally . in structural engineering and building code publications. Engineers at all levels of their careers will find the determinate and indeter- minate analysis methods in the book presented in a. analysis, which I believe are becoming lost in structural engineering. Having a solid foundation in the fundamentals of analysis enables engineers to understand the behavior of structures and. 1.8 Structural Analysis: In Theory and Practice 8 Example 1.1 Determine the support reactions of the pin-jointed truss shown in Figure 1.9 . End 1 of the truss has a hinged support, and end