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Fundamentals of structural dynamics

Fundamentals of Structural Analysis P1 docx

Fundamentals of Structural Analysis P1 docx

... have a direct bearing on the design of the content of a course in structural analysis: the reduction of credit hours to three required hours in structural analysis in most civil engineering curricula ... four DOFs, since each node has two DOFs and there are two nodes for each member We may also use the way each of the DOF is sequenced to refer to a particular DOF For example, the second DOF of member ... truss is composed of relatively slender members often forming triangular configurations An example of a plane truss used in the roof structure of a house is shown below A roof truss called Fink...
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Fundamentals of Structural Analysis P2 doc

Fundamentals of Structural Analysis P2 doc

... are changed by the addition of one more diagonal member (9) Concluding remarks If the number of nodes is N and the number of constrained DOF is C, then (a) the number of simultaneous equations ... determined The resulting method of analysis is simple and straightforward and is very easy to be implemented into a computer program As a matter of fact, virtually all structural analysis computer packages ... Truss Analysis: Matrix Displacement Method by S T Mau Kinematic instability resulting from insufficient number of supports or members Problem 4: Discuss the kinematic stability of each of the...
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Fundamentals of Structural Analysis Episode 1 Part 1 docx

Fundamentals of Structural Analysis Episode 1 Part 1 docx

... from each of the three nodes NODE FBD Py2 (Fx2 )1+ (Fx2)2 Px2 (Fy2 )1+ (Fy2)2 (Fy2 )1 (Fy2)2 2 (Fy1 )1 (Fy3)2 (Fx1 )1 (Fx3)2 3 Py1 (Fx1 )1+ (Fx1)3 (Fx2)2 (Fx2 )1 Px1 (Fy1 )1+ (Fy1)3 (Fy1)3 (Fx1)3 Py3 (Fx3)2+ ... 93 94 10 1 10 2 10 9 11 8 Beam and Frame Analysis: Force Method, Part II Deflection of Beam and Frames Problem 12 1 12 1 13 2 iii Problem Problem 14 3 15 2 Beam and Frame Analysis: Force Method, Part III ... ⎧ Fx1 ⎫ ⎪F ⎪ ⎪ y1 ⎪ ⎨ ⎬= ⎪ Fx ⎪ ⎪ Fy ⎪ ⎩ ⎭ ⎡ k 11 ⎢k ⎢ 21 ⎢ k 31 ⎢ ⎣k 41 k12 k13 k 22 k 32 k 42 k 23 k 33 k 43 k14 ⎤ k 24 ⎥ ⎥ k 34 ⎥ ⎥ k 44 ⎦ ⎧u1 ⎫ ⎪v ⎪ ⎪ 1 ⎨ ⎬ ⎪u ⎪ ⎪v ⎪ ⎩ ⎭ (12 ) Truss Analysis: ...
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Fundamentals of Structural Analysis Episode 1 Part 1 pptx

Fundamentals of Structural Analysis Episode 1 Part 1 pptx

... from each of the three nodes NODE FBD Py2 (Fx2 )1+ (Fx2)2 Px2 (Fy2 )1+ (Fy2)2 (Fy2 )1 (Fy2)2 2 (Fy1 )1 (Fy3)2 (Fx1 )1 (Fx3)2 3 Py1 (Fx1 )1+ (Fx1)3 (Fx2)2 (Fx2 )1 Px1 (Fy1 )1+ (Fy1)3 (Fy1)3 (Fx1)3 Py3 (Fx3)2+ ... 93 94 10 1 10 2 10 9 11 8 Beam and Frame Analysis: Force Method, Part II Deflection of Beam and Frames Problem 12 1 12 1 13 2 iii Problem Problem 14 3 15 2 Beam and Frame Analysis: Force Method, Part III ... ⎧ Fx1 ⎫ ⎪F ⎪ ⎪ y1 ⎪ ⎨ ⎬= ⎪ Fx ⎪ ⎪ Fy ⎪ ⎩ ⎭ ⎡ k 11 ⎢k ⎢ 21 ⎢ k 31 ⎢ ⎣k 41 k12 k13 k 22 k 32 k 42 k 23 k 33 k 43 k14 ⎤ k 24 ⎥ ⎥ k 34 ⎥ ⎥ k 44 ⎦ ⎧u1 ⎫ ⎪v ⎪ ⎪ 1 ⎨ ⎬ ⎪u ⎪ ⎪v ⎪ ⎩ ⎭ (12 ) Truss Analysis: ...
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Fundamentals of Structural Analysis Episode 1 Part 2 pot

Fundamentals of Structural Analysis Episode 1 Part 2 pot

... 31 ⎪ ⎪ ⎢ ⎪ Fy ⎪ ⎢k 41 ⎩ ⎭ ⎣ 0 0 0 k 11 k 21 k 31 k 41 k 12 k 22 k 32 k 42 k13 k 23 k 33 k 43 0 0 0 k13 k 23 0 k 12 k 22 0 k 32 k 42 0 0 0 k 33 k 43 ⎤ ⎧u1 ⎫ ⎥ ⎪ v1 ⎪ ⎥ ⎪ ⎪ ⎪ ⎪ k14 ⎥ ⎪u ⎪ ⎥ ⎨ ⎬ k 24 ... equation: ⎡ K 11 ⎢K ⎢ 21 ⎢ K 31 ⎢ ⎢ K 41 ⎢ K 51 ⎢ ⎢ K 61 ⎣ K 12 K 22 K 32 K 42 K 52 K 62 K 13 K 23 K 33 K 43 K 53 K 63 K 14 K 24 K 34 K 44 K 54 K 64 K 15 K 25 K 35 K 45 K 55 K 65 K 16 ⎤ K 26 ⎥ ⎥ K ... S2 − CS − S2 −C2 − CS C2 CS − CS ⎤ ⎥ − S2⎥ = CS ⎥ ⎥ S 1 ⎦ 9.6 − 7 .2 − 9.6⎤ ⎡ 7 .2 ⎢ 9.6 12 .8 − 9.6 − 12 .8⎥ ⎢ ⎥ ⎢− 7 .2 − 9.6 7 .2 9.6⎥ ⎢ ⎥ 9.6 12 .8⎦ ⎣ − 9.6 − 12 .8 ⎡ C2 ⎢ EA ⎢ CS )2 (kG )2= ( L ⎢−...
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Fundamentals of Structural Analysis Episode 1 Part 3 pps

Fundamentals of Structural Analysis Episode 1 Part 3 pps

... (2-c) kN 1. 5m kN kN 3m 3m 3m 2m 4m 4m (3- a) (3- b) 1. 2 m kN 4kN 5kN kN 1. 6 m (4-a) 0.7 m 0.9 m 0.9 m 0.7 m 0.9 m 0.9 m 0.9 m 2m (3- c) 1. 2 m 1. 2 m 3m 3m (4-b) (4-c) kN kN 2m 2m kN 1m 1m 1m 1m 2m 2m ... Fy = 0, F5 (3/ 5) – F4 (3/ 5) –F1= 0, F1= –6 kN 38 Truss Analysis: Force Method, Part I by S T Mau Joint Σ Fx = 0, 4 F6(4/5) + F3(4/5) =0, F3 = kN Σ Fy = 0, F6 F6 (3/ 5) – F3 (3/ 5) –F2= 0, F3 F2 F2= –6 ... F2= –6 kN Joint Σ Fx = 0, F1 Rx1+ F3(4/5) =0, Σ Fy = 0, Ry1+F3 (3/ 5) +F1= 0, F3 Rx1 Ry1 Ry1= kN Joint Σ Fx = 0, 5 Rx5 Rx5 – F4(4/5) =0, Σ Fy = 0, F2 F4 Rx1 = –4 kN Ry5+F4 (3/ 5) +F2= 0, Rx5 = kN Ry5...
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Fundamentals of Structural Analysis Episode 1 Part 3 pps

Fundamentals of Structural Analysis Episode 1 Part 3 pps

... (2-c) kN 1. 5m kN kN 3m 3m 3m 2m 4m 4m (3- a) (3- b) 1. 2 m kN 4kN 5kN kN 1. 6 m (4-a) 0.7 m 0.9 m 0.9 m 0.7 m 0.9 m 0.9 m 0.9 m 2m (3- c) 1. 2 m 1. 2 m 3m 3m (4-b) (4-c) kN kN 2m 2m kN 1m 1m 1m 1m 2m 2m ... Fy = 0, F5 (3/ 5) – F4 (3/ 5) –F1= 0, F1= –6 kN 38 Truss Analysis: Force Method, Part I by S T Mau Joint Σ Fx = 0, 4 F6(4/5) + F3(4/5) =0, F3 = kN Σ Fy = 0, F6 F6 (3/ 5) – F3 (3/ 5) –F2= 0, F3 F2 F2= –6 ... F2= –6 kN Joint Σ Fx = 0, F1 Rx1+ F3(4/5) =0, Σ Fy = 0, Ry1+F3 (3/ 5) +F1= 0, F3 Rx1 Ry1 Ry1= kN Joint Σ Fx = 0, 5 Rx5 Rx5 – F4(4/5) =0, Σ Fy = 0, F2 F4 Rx1 = –4 kN Ry5+F4 (3/ 5) +F2= 0, Rx5 = kN Ry5...
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Fundamentals of Structural Analysis Episode 1 Part 4 pps

Fundamentals of Structural Analysis Episode 1 Part 4 pps

... Denoting the elongation of memebr as V3 We have (a) V3= α (∆T)L= 1. 2 (10 -5)/oC ( 14 oC) (6,000 mm)= 1mm (b) V3=1mm (c) V3= 16 kN (6 m)/[200 (10 6) kN/m2 (500) (10 -6)m2]=0.0 01 m= 1mm Next we need to find ... Example 11 only in the externally applied loads Use the force transfer matrix of Eq to find the solution 1. 0 kN 0.5 kN y x 4m 3 3m 3m Problem 4- 2 66 1. 0 kN Truss Analysis: Force Method, Part II ... units are added by the user: F1= −0. 21 kN; F2= 1. 04 kN; F3= 0.62 kN; F4= −0.50 kN; F5= 0 .17 kN; F6= 0.83 kN; 60 Truss Analysis: Force Method, Part I by S T Mau Problem (1) The loaded truss shown...
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Fundamentals of Structural Analysis Episode 1 Part 4 pptx

Fundamentals of Structural Analysis Episode 1 Part 4 pptx

... Denoting the elongation of memebr as V3 We have (a) V3= α (∆T)L= 1. 2 (10 -5)/oC ( 14 oC) (6,000 mm)= 1mm (b) V3=1mm (c) V3= 16 kN (6 m)/[200 (10 6) kN/m2 (500) (10 -6)m2]=0.0 01 m= 1mm Next we need to find ... Example 11 only in the externally applied loads Use the force transfer matrix of Eq to find the solution 1. 0 kN 0.5 kN y x 4m 3 3m 3m Problem 4- 2 66 1. 0 kN Truss Analysis: Force Method, Part II ... units are added by the user: F1= −0. 21 kN; F2= 1. 04 kN; F3= 0.62 kN; F4= −0.50 kN; F5= 0 .17 kN; F6= 0.83 kN; 60 Truss Analysis: Force Method, Part I by S T Mau Problem (1) The loaded truss shown...
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Fundamentals of Structural Analysis Episode 1 Part 5 pdf

Fundamentals of Structural Analysis Episode 1 Part 5 pdf

... -56 .56 40.00 -56 .56 -40.00 25, 000 25, 000 25, 000 17 ,680 25, 000 17 ,680 25, 000 17 ,680 25, 000 3.20 3.20 1. 60 -6.40 4.80 -3.20 1. 60 -3.20 -1. 60 0.00 -0. 71 0.00 0.00 -0. 71 1.00 -0. 71 0.00 -0. 71 -0.33 -0.33 ... -0.8 -0.032 0.026 0 .50 33,333 0. 0 15 -0.6 -0.009 -0. 018 0. 011 -0.83 20,000 -0.042 1. 0 -0.042 0. 050 0. 050 20,000 1. 0 0. 050 0. 050 (kN/m) Vι (mm) -0.33 25, 000 fi For δ Σ -0.040 0 .17 4 Note: Fi = ith ... Application of the energy conservation principle leads to 1 (1) ∆o' + 2 n M ∑ P ∆i + (1) (∆o) = ∑ f i i =1 j =1 j vj + M M ∑F V +∑ f V j =1 j j j =1 j j (17 ) Substracting Eq 17 by Eq 15 and Eq 16 yields...
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Fundamentals of Structural Analysis Episode 1 Part 5 pps

Fundamentals of Structural Analysis Episode 1 Part 5 pps

... -56 .56 40.00 -56 .56 -40.00 25, 000 25, 000 25, 000 17 ,680 25, 000 17 ,680 25, 000 17 ,680 25, 000 3.20 3.20 1. 60 -6.40 4.80 -3.20 1. 60 -3.20 -1. 60 0.00 -0. 71 0.00 0.00 -0. 71 1.00 -0. 71 0.00 -0. 71 -0.33 -0.33 ... -0.8 -0.032 0.026 0 .50 33,333 0. 0 15 -0.6 -0.009 -0. 018 0. 011 -0.83 20,000 -0.042 1. 0 -0.042 0. 050 0. 050 20,000 1. 0 0. 050 0. 050 (kN/m) Vι (mm) -0.33 25, 000 fi For δ Σ -0.040 0 .17 4 Note: Fi = ith ... Application of the energy conservation principle leads to 1 (1) ∆o' + 2 n M ∑ P ∆i + (1) (∆o) = ∑ f i i =1 j =1 j vj + M M ∑F V +∑ f V j =1 j j j =1 j j (17 ) Substracting Eq 17 by Eq 15 and Eq 16 yields...
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Fundamentals of Structural Analysis Episode 1 Part 6 doc

Fundamentals of Structural Analysis Episode 1 Part 6 doc

... M=2, N=3, C =1 R =1 R =1 Number of unknowns = 3M+ΣR =12 , Number of equations = 3N+ΣC= 11 Indeterminate to the 1st degree Number of unknowns = 3M+ΣR =10 , Number of equations = 3N+C= 10 Statically ... M=5, N =6, C=2 M=3, N=4, C =1 R=3 R=2 R=3 R=3 R=2 R =1 Number of unknowns = 3M+ΣR = 21, Number of equations = 3N+C = 20 Indeterminate to the 1st degree Number of unknowns 3M+ΣR =15 , Number of equations ... right 10 7 Beam and Frame Analysis: Force Method, Part I by S T Mau (3) Draw the moment diagram from left to right 15 kN M 13 .5 kN-m -6 kN/m kN/m 2m 3m 2m 3m 1. 5 kN M -12 kN/m -12 kN/m Drawing moment...
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Fundamentals of Structural Analysis Episode 1 Part 6 pdf

Fundamentals of Structural Analysis Episode 1 Part 6 pdf

... M=2, N=3, C =1 R =1 R =1 Number of unknowns = 3M+ΣR =12 , Number of equations = 3N+ΣC= 11 Indeterminate to the 1st degree Number of unknowns = 3M+ΣR =10 , Number of equations = 3N+C= 10 Statically ... M=5, N =6, C=2 M=3, N=4, C =1 R=3 R=2 R=3 R=3 R=2 R =1 Number of unknowns = 3M+ΣR = 21, Number of equations = 3N+C = 20 Indeterminate to the 1st degree Number of unknowns 3M+ΣR =15 , Number of equations ... right 10 7 Beam and Frame Analysis: Force Method, Part I by S T Mau (3) Draw the moment diagram from left to right 15 kN M 13 .5 kN-m -6 kN/m kN/m 2m 3m 2m 3m 1. 5 kN M -12 kN/m -12 kN/m Drawing moment...
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