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engineering
fundamentals of structural analysis

Fundamentals Of Structural Analysis 5th Edition Kenneth Leet, Chia-Ming Uang, Joel Lanning - Solutions

If member \(A B\) in Figure \(\mathrm{P} 10.25\) is fabricated \(\frac{3}{4}\) in. too long, determine the moments and reactions created in the frame when it is erected. Sketch the deflected shape. Given: \(E=29,000\) kips/in. \({ }^{2}\). 12' B /= 120 in. I=240 in 4 24 C
Analyze the frame in Figure P10.26.Given: \(E I\) is constant. 1 kip/ft, w = 1 kip/ft B 108 A 44 -25'- C T 10' 20'
Analyze the frame in Figure P10.27.Note that support \(D\) can translate in the horizontal direction only. Compute all reactions and draw the shear and moment curves. Given: \(E=29,000 \mathrm{ksi}\) and \(I=100 \mathrm{in} .{ }^{4}\). 3' 5' 100 kips A C I B I 21 8' D
Analyze the frame in Figure P10.28.Notice that sidesway is possible because the load is unsymmetric. Compute the horizontal displacement of joint \(B\). Given: \(E=29,000 \mathrm{kips} / \mathrm{in} .{ }^{2}\) and \(I=240 \mathrm{in} .{ }^{4}\) for all members. B A 30 kips H 20 D 12'
Analyze the frame in Figure P10.29.Compute all reactions. Use \(I_{B C}=200 \mathrm{in} .{ }^{4}\) and \(I_{A B}=I_{C D}=150 \mathrm{in} .{ }^{4}\). \(E\) is constant. A B 100 kip.ft 1520 D 20' -9-1 20
Determine all reactions at points \(A\) and \(D\) in Figure P10.30.EI is constant. 60 KN 8 m B 10 m C D 6 m
Analyze the frame in Figure P10.31.EI is constant. 70 KN A B 5m C D I 3 m 3 m
Set up the equilibrium equations required to analyze the frame in Figure P10.32 by the slope deflection method. Express the equilibrium equations in terms of the appropriate displacements. \(E I\) is constant for all members. 20' B A -10% 40 kips 10'- C 15'
Set up the equilibrium equations required to analyze the frame in Figure P10.33 by the slopedeflection method. Express the equilibrium equations in terms of the appropriate displacements. EI is constant for all members. 2 kips A B to w = 2 kips/li 16' E D 7 12' 8'
Set up the equilibrium equations required to analyze the frame in Figure 10.34 by the slope-deflection method. Express the equilibrium equations in terms of the appropriate displacements. EI is constant for all members. B -12 50 kips 12'- D C 10' 10'
Determine the degree of kinematic indeterminacy for each structure in Figure P10.35.Neglect axial deformations. A CON B (a) B 3 IT CREARE B B (P) RECUSANA SECCIONS PERM H F
Using the law of sines, resolve the 75-lb vertical force FAB in Figure 3.3 into components directed along lines a and b.Figure 3.3 FAC, 80 FCB 60 A 40 B 30 FAR=75 lb (b) 50 FAB=75 lb B 50 (a)
Determine the magnitude and location of the resultant R of the three wheel loads shown in Figure 3.4.Figure 3.4 20 KN 3 m R = 50 kN 20 kN B 2m 10 kN
Compute the magnitude and location of the resultant of the parabolic loading shown in Figure 3.6. The slope of the parabola is zero at the origin.Figure 3.6 0 = L R
The beam in Figure 3.7a supports a distributed load whose ordinates lie on a parabolic curve. Replace the distributed load by a statically equivalent set of concentrated loads.Figure 3.7a 10% W + 6.25 16/2 555 5' (a) W3, W4 12.25 15' P P P (b) P 105-5-5-
Compute the reactions for the beam in Figure 3.18a.Figure 3.18a 10' B 5-10 kips 5'-
Compute the reactions for the truss in Figure 3.19.Figure 3.19 B D P = 18 kips C Cy 6 C
The frame in Figure 3.20 carries a distributed load that varies from 4 to 10 kN/m. Compute the reactions.Figure 3.20 10 kN/m B R 6m R 20 E x = 5m C m 4 kN/m 8 m Cx
Compute the reactions for the beam in Figure 3.21a, treating member AB as a link.Figure 3.21a T link B 20 kip. ft pin -333 9 kips/ft c
Compute the reactions for the beam in Figure 3.22a. A load of 12 kips is applied directly to the hinge at C.Figure 3.22a A 10. B By hinge 24 kips D 12 kips 55: in E E Ex
Compute the reactions for the beams in Figure 3.23a.Figure 3.23a A A Ay -10- 25 kips B (a) 5 C Cy D -D,
Investigate the stability of the structure in Figure 3.27a. Hinges at joints B and D.Figure 3.27a A B -4- 4
Analyze the truss in Figure 4.11a by the method of joints. Reactions are given.Figure 4.11a 22 kips 24 kips M S 11' Di S 13, D 24 kips 12 6' 22 kips
Label all the bars in the truss of Figure 4.13 that are unstressed when the 60-kip load acts.Figure 4.13 60 kips B 0 MOL K J D 180 kips E - F G H 120 kips
Using the method of sections, compute the forces or components of force in bars HC, HG, and BC of the truss in Figure 4.14a.Figure 4.14a A, 60 kips IM F B E 3 @ 15' 45'- C D T 15' 5
Analyze the determinate truss in Figure 4.15a to determine all bar forces and reactions.Figure 4.15a A 60 kips Ay la F B E C 3 @ 15' 45' C Dy T 15' 1s 5'
Determine the forces in bars HG and HC of the truss in Figure 4.16a by the method of sections.Figure 4.16a RA = 60 kips H B 30 kips 3 C 60 kips 4 @ 24' = 96' D 30 kips E RE= 60 kips 6 18'
Using the method of sections, compute the forces in bars BC and JC of the K truss in Figure 4.17a.Figure 4.17a T 15' 15' L H 24 kips .00 B 100 48 kips 20+ 20'- K F 48 kips 20 E
Verify that the truss in Figure 4.19 is stable and determinate by demonstrating that it can be completely analyzed by the equations of statics for a force of 4 kips at joint F.Figure 4.19 I 12 0 4 kips 3 H +3 - B G 12 - P = 4 kips +3 F D 4 kips 4 kips 12 1212 -12121212 E T 16'
Prove that the given figure 4.20a as shown in the belowfigure 4.20 RAX RAY = 2 kips F B 3 kips E C 3 @ 10' 30'- D RDX Rp = 1 kip T 10'
Classify the trusses in Figure P4.1 as stable or unstable. If stable, indicate if determinate or indeterminate. If indeterminate, indicate the degree of indeterminacy.Figure P4.1 DRO (a) (b) (c) (d) P (e) pinned joint 69 (h)
Classify the trusses in Figure P4.2 as stable or unstable. If stable, indicate if determinate or indeterminate. If indeterminate, indicate the degree.Figure P4.2 ApaA (a) (c) (e) S (b) 888 63 (d) (h)
Determine the forces in all bars of the trusses. Indicate tension or compression. 4m B 3 m G 40 kN 3m D F 30 kN 3 m E 20 KN 15 kN
Determine the forces in all bars of the trusses. Indicate tension or compression. B 16 kips 9' 24 kips C 9 60 kips D H + 9' 36 kips E G 9' 24 kips 12
Determine the forces in all bars of the trusses. Indicate tension or compression. I D 20 kN -5 @ 5m= 25 m H 20 KN E G 20 KN -10 kN 5 m
Determine the forces in all bars of the trusses. Indicate tension or compression. 22.5'- E 60 kips 36 kips B D +7.5 15 15- 36 kips 20'
Determine the forces in all bars of the trusses. Indicate tension or compression. 20' -20% 0: C if D F = 100 kips T 20' 15'
Determine the forces in all bars of the trusses. Indicate tension or compression. 6 m 6 m B 30 kN 60 kN 6m
Determine the forces in all bars of the trusses. Indicate tension or compression. 8 kips 16'- C D 36 kips + 16' T 12' E 12' B -24 kips
Determine the forces in all bars of the trusses. Indicate tension or compression. 15' G F B 24 kips E 3 @ 10' = 30' D 24 kips
Determine the forces in all bars of the trusses. Indicate tension or compression. 15 B F 10 kips 1 15'- E + 20 kips 15' 15'
Determine the forces in all bars of the trusses. Indicate tension or compression. 36 kips 15' 15' B H 15'- C G F D -15 15 24 kips VE 20'
Determine the forces in all bars of the trusses. Indicate tension or compression. 10 kips B H 10 kips G 4 @ 8' 32' 10 kips D F 4 kips E 6'
Determine the forces in all bars of the trusses. Indicate tension or compression. B 60 kips H 4 @ 20' 80' L G D F 15' 15' E
Determine the forces in all bars of the trusses. Indicate tension or compression. A 16' 32 kips H B 64 kips G C 16' + 16- D 16'- E 16' 8
Determine the forces in all bars of the truss. Hint: If you have trouble computing bar forces, review K truss analysis in Example 4.6.Example 4.6Using the method of sections, compute the forces in bars BC and JC of the K truss in Figure 4.17a.Figure 4.17a B L 3 m C -3 m H K D 3 m. G E 60 kN 60 kN 3
Determine the forces in all bars of the trusses. Indicate tension or compression. 15 kips T 10' # 10' B 20 kips HG F 4 @ 10' 40' 10 kips D E
Determine the forces in all bars of the trusses. Indicate tension or compression. B 60 kips 20' G 20' F 60 kips 20' E T 15' 30 kips 15'
Determine the forces in all bars of the trusses. Indicate tension or compression. B 3m4m-3m- 60 KN E C D
Determine the forces in all bars of the trusses. Indicate tension or compression. A B C 100 KN 4m- D H E 4 m F RG T 4 m 4 m 4 m
Determine the forces in all bars of the trusses. Indicate tension or compression. 4m4m- B G 24 kN 8 m C 30 kN 4m4m- D 6 m
Determine the forces in all truss bars. Indicate tension or compression. 10 KN B H 6 kN G 4 @4m F D E 3 m 3 m
Determine the forces in all truss bars. Indicate tension or compression. 60 KN 45 kN 30 kN 6m C 6m B 6 m 8 m E J 10 m G
Determine the forces in all truss bars. Indicate tension or compression. G H 8 m F I 30 kN + 2 8 m K L E 8 m D 6 m C+12 kN 6 m 6 kN B12 KN 6 m
Determine the forces in all truss bars. Indicate tension or compression. 10' A to B D E M WAA Q H '30 k 8 @ 10' = 80' K 10 k P 10 k R 20' G
Determine the forces in all truss bars. Indicate tension or compression. 90 KN 60 kN 30 kN B A D -8 m E F 6m RH 6 m dG+ 6 m
Determine the forces in all bars of the truss in Figure P4.27. If your solution is statically inconsistent, what conclusions can you draw about the truss? How might you modify the truss to improve its behavior? Also, analyze the truss with your computer program. Explain your results. A B C 40 kN 40
Determine the forces in all bars. Indicate tension or compression. 12 kN B G 18 KN 3@4m F 12 KN E T 2 m 2 m
Determine the forces in all bars. Indicate tension or compression. 24 kips B G 24 kips C 24 kips | 101010 E H T 10' 10'
Determine the forces in all bars. Indicate tension or compression. T 20 20 L C D A 15' B 40 kips E
Determine the forces in all bars. Indicate tension or compression. 6 kips 12'- 12 kips to 12' B T 6' 9'
Determine all bar forces. Indicate tension or compression. 20 KN H G 24 kN 4 @ 5m 20 KN D E T 5 m 5 m
Determine all bar forces. Indicate tension or compression. B G A 30 kips 6 kips 5. F E 810108 12' 8'
Determine all bar forces. Indicate tension or compression. 20 KN B 40 KN M 40 kN N L D 40 KN K E 6 @4m 40 kN 40 KN G 20 KN H 1 3 m 4 m
Using the method of sections, determine the forces in the bars listed below each figure. 20 kips B C 40 kips E F - 4 @ 15' = 60' AB, BD, AD, BC, and EF 20 kips G H T 10' 1 10
Using the method of sections, determine the forces in the bars listed below each figure. B C D 53 6 @ 15' 90' BL, KJ, JD, and LC E 30 kips 90 kips 30 kips H G TH 3 6' 12'
Using the method of sections, determine the forces in the bars listed below each figure. 30 kips H 18 kips E -3@12= 36- EF. EI, ED, FH, and II -12 kips T 9 204 D +*+ 16
Using the method of sections, determine the forces in the bars listed below each figure. B 30 kips H D 60 kips 5 @ 15' BJ, CJ, CI, HG, and DI E F 20'
Using the method of sections, determine the forces in the bars listed below each figure. L K M B 12 kN C 16 KN 4@4m IJ, MC, and MI H N D 12 kN G E T 3 m 3 m
Determine the forces in all bars of the trusses in Figure P4.40. Indicate if bar forces are tension or compression. 3m 3 m B F 30 kN 3 m E 3 m T D T 2m
Determine the forces in all bars of the trusses in Figure P4.41. Indicate if bar forces are tension or compression. K B 30 kips H C 60 kips 4 @ 20 L G D 30 kips F E T 15' 15' 1
Determine the forces in all bars of the trusses in Figure P4.42. Indicate if bar forces are tension or compression. 24 kips E W 969 B 12' +4 12'
Determine the forces or components of force in all bars of the trusses in Figure P4.43. Indicate tension or compression. Let T 2m 2m 2m A 5m 16 kN F B 5 16 kN G 5 m- 8 kN H D 5 m- E
Determine the forces or components of force in all bars of the trusses in Figure P4.44. Indicate tension or compression. T 12' L E D 6 kips F 12 kips G B 18 kips 3 @ 18' 54' H T 12' 12'
Determine the forces or components of force in all bars of the trusses in Figure P4.45. Indicate tension or compression. 12 kN B G 6 kN 4@4m 12 kN D F E I 3 m
Determine the forces or components of force in all bars of the trusses in Figure P4.46. Indicate tension or compression. 3.6 kips 1.8 kips 7.2 kips B 2.4 kips 2.4 kips G 7.4 kips 2.4 kips D 88 8 + 8 T 6' 6'
Determine the forces or components of force in all bars of the trusses in Figure P4.47. Indicate tension or compression. 12 kips B 12 kips 12 kips 4 @ 8' 32' 12 kips H E 12 kips F G Tatatad
Determine the forces or components of force in all bars of the trusses in Figure P4.48. Indicate tension or compression. 40' B 40' C 30 kips 40' 30' 30'
Determine the forces or components of force in all bars of the trusses in Figure P4.49. Indicate tension or compression. 3 m A 30 kN 4 m F B 60 kN + 4 m Je 4 m 2 m 2m
Determine the forces or components of force in all bars of the trusses in Figure P4.50. Indicate tension or compression. 8 KN 12 kN -5 m 12 kN 6 kN -- 2m -- 2m -- 2m -- 2m - 5 m 2 m EL 3 m 2 m
Determine the forces or components of force in all bars of the trusses in Figure P4.51. Indicate tension or compression. 20 kN B 90 20 KN 90 60 kN 4 @4m E H F G 3m 3 m
A two-lane highway bridge, supported on two deck trusses that span 64 ft, consists of an 8-in. reinforced concrete slab supported on four steel stringers. The slab is protected by a 2-in. wearing surface of asphalt. The 16-ft-long stringers frame into the floor beams, which in turn transfer the
Computer analysis of a truss. The purpose of this study is to show that the magnitude of the joint displacements as well as the magnitude of the forces in members may control the proportions of structural members. For example, building codes typically specify maximum permitted displacements to
Computer study. The objective is to compare the behavior of a determinate and an indeterminate structure. The forces in members of determinate trusses are not affected by member stiffness. Therefore, there was no need to specify the cross-sectional properties of the bars of the determinate trusses
Computer analysis of a truss with rigid joints. The truss in Figure P4.55 is constructed of square steel tubes welded to form a structure with rigid joints. The top chord members 1, 2, 3, and 4 are 4×4×1/4 square tubes with A = 3.37 in.2 and I = 7.80 in.4. All other members are 3×3×1/4 square
Analyze and compare two trusses, arched configurations of the Pratt Truss and the Howe Truss in Figures P4.56 (a) and (b), respectively. The trusses have the same depth, length, panel spacing, loading, and supports. All joints are pinned. For each truss, do the following. a) Compute all bar forces
Write the equations for the variation of shear V and moment M along the axis of the cantilever beam in Figure 5.7. Using the equation, compute the moment, 4 ft to the right of point B.Figure 5.7 P = 4 kips A 4 kips A 4 kips 4 kips (b) V M (a) 2 kips/ft B (c) R = 2x (d) w = 2 kips/ft X2 2 kips/ft
For the beam in Figure 5.8 write the expressions for moment between points B and C, using an origin located at (a) support A, (b) support D, and (c) point B. Using each of the expressions above, evaluate the moment. Shear force on sections is omitted for clarity.Figure 5.8 37 kips 37 kips 37 kips w
Write the equations for shear and moment as a function of distance x along the axis of the beam in Figure 5.9. Select the origin at support A. Plot the individual terms in the equation for moment as a function of the distance x.Figure 5.9 +M M W R= M M= W (4) (b) WX2 (c) (d) M S R =
(a) Write the equations for shear and moment on a vertical section between supports B and C for the beam in Figure 5.10a.(b) Using the equation for shear in part (a), determine the point where the shear is zero (the point of maximum moment).(c) Plot the variation of the shear and moment between
Write the equations for moment in members AC and CD of the frame in Figure 5.11. Draw a free body of joint C, showing all forces.Figure 5.11 3 m 3 m 20 KN A, = 9.2 kN B 6 m V = 7.64 KN (a) F= 20.64 kN 6.5 KN w = 4 kN/m 14.14 KN 14.14 KN 4 m 6.5 kN (c) 4.8 kN.m 32 (e) X3 4.8 kN.m D, = 6.8 kN M 3+
Draw the shear and moment curves for the simply supported beam in Figure 5.14.Figure 5.14 R = 21.5 kips 21.5 R = 24 kips 6' (115.56) w = 2 kips/ft 12' x= 10.75- R = 21.5 kips B (a) (-1.56) (b) 1.25 (c) (d) P = 13.5 kips 40 kip.ft 21.5 115.56 114 74 R = 2x (e) +4+4- (-10) -2.5 Rc = 16 kips 2.5 (-64)
Draw the shear and moment curves for the uniformly loaded beam in Figure 5.15a. Sketch the deflected shape.Figure 5.15a. R = 6(24) 144 kips w = 6 kips/ft 6+ B 96 kips = Rg (a) 18' 12' TEN - C 48 kips = Re
Draw the shear and moment curves for the inclined beam in Figure 5.16a.Figure 5.16a RA 8- 40 kips 16' B Ra 12'
Draw the shear and moment curves for the beam in Figure 5.17a. Sketch the deflected shape.Figure 5.17a M = 148 kip.ft A 10 kips R = 20.8 kips hinge B 54 kips w = 9 kips/ft 27 kips 46-46 2 Re= 70.2 kips -6- D
Draw the shear and moment curves for beam ABC in Figure 5.18a. Also sketch the deflected shape. Rigid joints connect the vertical members to the beam. Elastomeric pad at C equivalent to a roller.Figure 5.18a RAX A RAY 8' 5 kips E B 15 kips 30 kips 12' D Re
Draw the shear and moment curves and sketch the deflected shape of the continuous beam in Figure 5.19a. The support reactions are given.Figure 5.19a 13.1 kips 40 kips 57.67 kips 88 w = 3 kips/ft 207 Mc94.84 (kip.ft) 29.23 kips
Draw the shear and moment curves for each member of the frame in Figure 5.20, and sketch the deflected shape.Figure 5.20 T 20 kips L 100 B RAY 20 moment shear (kip.ft) (kips) w = 2 kips/ft -RAX 10 100 moment (kip.ft) 8.89 shear (kips) 20 kips 4.45% 119.78 w=2 kips/ft -11.11 20 kips 8.89 kips
Draw the shear and moment curves for each member of the frame in Figure 5.21a. Also sketch the deflected shape and show the forces acting on a free body of joint C. Treat the connection at B as a hinge.Figure 5.21a 12 5 kips/ft 12 38.7 kips T Ta4a4
(a) Evaluate the reactions and construct the moment diagram for the beam in Figure 5.25a by superposition of the reactions and moment curves associated with the individual loads in parts (b), (c), and (d). (b) Calculate the moment of the area under the moment diagram between the left support and

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