Questions and Answers of Fundamentals Of Structural Analysis

Compute the deflection at midspan and the slope at \(A\) in Figure P8.19.EI is constant. Express the slope in degrees and the deflection in inches. Assume a pin support at \(A\) and a roller at \(D .
(a) Compute the vertical deflection and slope of the cantilever beam at points \(B\) and \(C\) in Figure P8.20.Given: \(E I\) is constant throughout, \(L=12 \mathrm{ft}\), and \(E=\) \(4000
Compute the deflection at \(B\) and the slope at \(C\) in Figure P8.21.Given: \(E I\) is constant. 3 kips/ft 15' B 15'- 85 kip. ft
Determine the value of moment that must be applied to the left end of the beam in Figure P8.22 if the slope at \(A\) is to be zero. \(E I\) is constant. Assume rocker at support \(D\) acts as a
Compute the vertical deflection of point \(C\) in Figure P8.23.Given: \(I=1200\) in. \(^{4}, E=29,000\) kips/in. \({ }^{2}\). A 21 12- w = 1.2 kips/ft B to 1 P = 6 kips 8' C
Compute the deflection at midspan of the beam in Figure P8.24.Given: \(I=46 \times 10^{6} \mathrm{~mm}^{4}, E=200 \mathrm{GPa}\). Treat rocker at \(E\) as a roller. B P = 18 kN te D 21 2 m-42 m-42
Under the dead load of the arch in Figure P8.25, the hinge at \(B\) is expected to displace 3 in. downward. To eliminate the 3 -in. displacement, the designers will shorten the distance between
If supports \(A\) and \(E\) in Figure \(\mathrm{P} 8.26\) are constructed \(30 \mathrm{ft}\) and \(2 \mathrm{in}\). apart instead of \(30 \mathrm{ft}\) apart, and if support \(E\) is also 0.75 in.
In Figure P8.27 support \(D\) is constructed 1.5 in. to the right of its specified location. Using Bernoulli's principle in Section 8.8, compute (a) the horizontal and vertical components of the
Compute the horizontal and vertical components of deflection at point \(D\) in Figure P8.28.\(E I\) is constant, \(I=120\) in. \(^{4}, E=29,000\) kips/in. \({ }^{2}\). A 3 kips |8| 5 kips B D -83 C
Compute the horizontal and vertical components of the deflection at \(C\) in Figure P8.29.\(E=200 \mathrm{GPa}, A=\) \(25 \times 10^{3} \mathrm{~mm}^{2}\), and \(I=240 \times 10^{6}
Compute the vertical displacement of joints \(B\) and \(C\) for the frame shown in Figure P8.30.Given: \(I=360\) in. \({ }^{4}, E=30,000 \mathrm{kips} / \mathrm{in} .{ }^{2}\). Consider only flexural
For the steel rigid frame in Figure P8.31, compute the rotation of joint \(B\) and the horizontal displacement of support \(C\). Given: \(E=200 \mathrm{GPa}, A=500 \mathrm{~mm}^{2}\), \(I=200 \times
(a) Compute the slope at \(A\) and the horizontal displacement of joint \(B\) in Figure P8.32.\(E I\) is constant for all members. Consider only bending deformations. Given: \(I=100\) in. \({ }^{4},
For the frame in Figure P8.33, compute the horizontal and vertical displacements at joint \(B\). Given: \(I=150\) in. \({ }^{4}, E=29,000 \mathrm{kips} / \mathrm{in} .{ }^{2}\). Consider only the
(a) Compute the vertical displacement of the hinge at \(C\) in Figure P8.34.\(E I\) is constant for all members, \(E=\) \(200 \mathrm{GPa}, I=1800 \times 10^{6} \mathrm{~mm}^{4}\). (b) The designer
Compute the vertical displacement of point \(C\) for the beam in Figure P8.35.For the beam \(A=5000 \mathrm{~mm}^{2}\), \(I=360 \times 10^{6} \mathrm{~mm}^{4}\), and \(E=200 \mathrm{GPa}\). For the
Compute the vertical deflection of joint \(C\) in Figure P8.36.In member \(A B C\) consider only the strain energy associated with bending. Given: \(I_{A C}=340 \mathrm{in} .^{4}\), \(A_{B D}=5\) in.
Compute the vertical deflection at \(B\) and the horizontal deflection at \(C\) in Figure P8.37.Given: \(A_{C D}=3\) in. \({ }^{2}\), \(I_{A C}=160\) in. \({ }^{4}, A_{A C}=4\) in. \({ }^{2}\), and
Compute the vertical and horizontal deflection at \(B\) and at the midspan of member \(C D\) in Figure P8.38.Consider both axial and bending deformations. Given: \(E=29,000 \mathrm{kips} /
Beam \(A B C\) is supported by a three-bar truss at point \(C\) and at \(A\) by an elastomeric pad that is equivalent to a roller. (a) Compute the vertical deflection of point \(B\) in Figure P8.39
If the horizontal displacement of joint \(B\) of the frame in Figure P8.40 is not to exceed 0.36 in., what is the required \(I\) of the members? Bar \(C D\) has an area of \(4 \mathrm{in}^{2}\), and
For the steel frame in Figure P8.41, compute the horizontal displacement of joint \(B\). For member \(B C D\), \(A=6000 \mathrm{~mm}^{2}\) and \(I=600 \times 10^{6} \mathrm{~mm}^{4}\). For member \(A
Using a finite summation, compute the initial deflection at midspan for the beam in Figure P8.42.Given: \(E=3000 \mathrm{kips} / \mathrm{in}{ }^{2}\). Use 3 -ft segments. Assume \(I=0.5 I_{G}\). A 30
Using a finite summation, compute the initial deflection at point \(C\) for the tapered beam in Figure P8.43.\(E=24 \mathrm{GPa}\). Base your analysis on the properties of \(0.5 I_{G}\). 300 mm 6 m-
Computer study-Influence of supports on frame behavior. (a) Using the RISA-2D computer program, compute the initial elastic deflection at midspan of the girder in Figure P8.44, given that the support
Computer study—Truss Stiffening Strategy. For the truss in Example 8.7, use the RISA-2D computer program to (a) Recompute the vertical deflection of F if the areas of members BC, CD, DE, EF,
Compute the reactions, draw the shear and moment curves, and locate the point of maximum deflection for the beam in Figure P9.1.EI is constant. A 9'- P = 36 kips B
For the beam in Figure P9.2, compute the reactions, draw the shear and moment curves, and compute the deflection of the hinge at \(C\). Use \(E=29,000 \mathrm{ksi}\) and \(I=180\) in. \({ }^{4}\). A
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.3.EI is constant. A 5 m M= 30 kN.m B 5 m C
Compute the reactions for the beam in Figure P9.4.\(E I\) is constant. Use support \(B\) as the redundant. A 7' w = 3 kips/ft B 7' C
Compute the reactions, draw the shear and moment curves, and locate the point of maximum deflection for the beam in Figure P9.5.Repeat the computation if \(I\) is constant over the entire length.
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.6.EI is constant. 15 kips B 15 kips 612126
Recompute the reactions, draw the shear and moment curves for the beam in Figure P9.6 if support \(B\) settles by \(1.5 \mathrm{in}\).. Check and compare your answer to that obtained using RISA-2D,
Determine the reactions for the beam in Figure P9.8.When the uniform load is applied, the fixed support rotates clockwise \(0.003 \mathrm{rad}\) and support \(B\) settles 0.3 in. Given: \(E=30,000\)
(a) Recompute the reactions, draw the shear and moment curves for the beam in Figure P9.8 if segment \(A B\) has 1.5I. (b) Using RISA-2D, recompute the reactions and generate the shear and moment
(a) Solve Problem P9.1 for the loading shown if support \(C\) settles 0.25 in. when the load is applied. Use moment at support \(A\) as the redundant. Given: \(E=30,000\) kips/in. \({ }^{2}\) and
Assuming that no load acts, compute the reactions and draw the shear and moment curves for the beam in Figure P9.1 if support \(A\) settles 0.5 in. and support \(C\) settles 0.75 in. Given:
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.12.\(E\) is constant. w = 4 kN/m 21 6 m- B hinge C +3m+ 18 KN 1 -3m- 6 m D
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.13.EI is constant. The bolted web connection at \(B\) may be assumed to act as a hinge. Use the shear at hinge
(a) Determine the reactions and draw the shear and moment curves for the beam in Figure P9.14.Given: \(E I\) is constant, \(E=30,000 \mathrm{kips} / \mathrm{in} .^{2}\), and \(I=288 \mathrm{in} .{
(a) Compute all reactions for the beam in Figure P9.15 assuming that the supports do not move; EI is constant. (b) Repeat computations given that support \(C\) moves upward a distance of \(288 /(E
Determine all reactions and draw the shear and moment curves for the beam in Figure P9.16.EI is constant. 24'- B w = 1 kip/ft 16 C
(a) Assuming that no loads act in Figure P9.16, compute the reactions if support \(B\) is constructed 0.48 in. too low. Given: \(E=29,000 \mathrm{kips} / \mathrm{in} .{ }^{2}, I=300 \mathrm{in} .{
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.18.Given: EI is constant. Take advantage of symmetry and use the end moment as the redundant. m 20 KN B 3 m 20 kN
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.19.Given: EI is constant. Use the reactions at \(B\) as the redundants. A W L B
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.20.Given: \(E I\) is constant for the beam. \(E=200 \mathrm{GPa}, I=40 \times 10^{6} \mathrm{~mm}^{4}\). 5m. B 20
Compute the reactions and draw the shear and moment curves for the beam in Figure P9.21.In addition to the applied load, the support at \(C\) settles by \(0.1 \mathrm{~m}\). \(E I\) is constant for
Consider the beam in Figure P9.21 without the applied load and support settlement. Compute the reactions and draw the shear and moment curves for the beam if support \(A\) rotates clockwise by
Recompute the reactions for the beam in Figure 9.4 if a spring with \(K=235 \mathrm{kips} / \mathrm{in}\). is provided between support \(B\) and the midspan of the beam.Figure 9.4 A 7' w = 3 kips/ft
Consider the truss in Figure P9.24 without theapplied load. Determine the reactions and all bar forces for the truss if member \(A B\) is fabricated 0.25 in. too short. The area of all bars is \(5
Compute the reactions and bar forces in all members for the truss in Figure P9.24 if a downward load of 120 kips is applied at joint \(E\). The area of all bars is 5 in. \(^{2}\) and \(E=30,000\)
Assuming that the 120-kip load is removed from the truss in Figure P9.24, compute the reactions and bar forces if the temperature of bars \(A B\) and \(B C\) increases \(60^{\circ} \mathrm{F}\); the
For the trusses in Figure P9. 27, compute the reactions and bar forces produced by the applied loads. Given: \(A E=\) constant, \(A=1000 \mathrm{~mm}^{2}\), and \(E=200 \mathrm{GPa}\). A 30 kN 8 m B
For the trusses in Figure P9. 28, compute the reactions and bar forces produced by the applied loads. Given: \(A E=\) constant, \(A=1000 \mathrm{~mm}^{2}\), and \(E=200 \mathrm{GPa}\). 6 m 8m B D 48
For the trusses in Figure P9. 29, compute the reactions and bar forces produced by the applied loads. Given: \(A E=\) constant, \(A=1000 \mathrm{~mm}^{2}\), and \(E=200 \mathrm{GPa}\). E 100 KN 60 KN
Determine the reactions and bar forces that are created in the truss in Figure P9.30 when the top chords \((A B C D)\) are subjected to a \(50^{\circ} \mathrm{F}\) temperature increase. Given: \(A
Determine the vertical and horizontal displacements at \(A\) of the pin-connected structure in Figure P9.31.Given: \(E=200 \mathrm{GPa}\) and \(A=500 \mathrm{~mm}^{2}\) for all members. -4m. B C A
Determine the vertical and horizontal displacements at \(A\) of the pin-connected structure in Figure P9.31.Given: \(E=200 \mathrm{GPa}, A_{A B}=1000 \mathrm{~mm}^{2}\), and \(A_{A C}=\) \(A_{A
(a) Determine all reactions and bar forces produced by the applied load in Figure P9.33.(b) If support \(B\) settles \(1 \mathrm{in}\). and support \(C\) settles \(0.5 \mathrm{in}\). while the load
Determine the reactions and all bar forces for the truss in Figure P9.34.\(E=29,000 \mathrm{ksi}\) and members \(A B\), \(B C, A D\), and \(D C\) have \(A=3\) in. \(^{2}\), and members \(B D, D E\),
Consider the truss in Figure P9.34 without the applied loads. Determine the reactions and all bar forces for the truss if supports \(A\) and \(C\) settle by 0.25 in.Figure P9.34 20%- B 20'- E 100
Determine the reactions and all bar forces for the truss in Figure P9.36.Given: \(E=200 \mathrm{GPa}\) and \(A=\) \(1000 \mathrm{~mm}^{2}\) for all bars. 40 KN 6 m- 80 KN D 3 E 4 m
Consider the truss in Figure P9.36 without the applied loads. Determine the reactions and all bar forces for the truss if support \(A\) settles by \(20 \mathrm{~mm}\).Figure P9.36 40 KN 6 m- 80 KN
Determine all bar forces and reactions for the truss in Figure P9.38.Given: area of bar \(B D=4\) in. \(^{2}\), all other bars \(=2\) in. \(^{2}\), and \(E=30,000\) kips/in. \({ }^{2}\). D 20' 15' B
Determine the reactions at \(A\) and \(C\) in Figure P9.39.\(E I\) is constant for all members. 9' 12' A B 60 kips 4.5' D
Determine all reactions for the frame in Figure P9.40 given \(I_{A B}=600\) in. \({ }^{4}, I_{B C}=900\) in. \({ }^{4}\), and \(E=29,000 \mathrm{kips} / \mathrm{in} .^{2}\). Neglect axial
Assuming that the load is removed, compute all reactions for the frame in Figure P9.40 if member \(B C\) is fabricated \(1.2 \mathrm{in}\). too long.Figure P9.40 B A 2 kips/ft 30'- C T 15'
(a) Compute the reactions in Figure P9.42.For all members, \(E=4000 \mathrm{ksi}\) and \(I=1000\) in. \({ }^{4}\). Spring \(C D\) has a stiffness of \(5 \mathrm{kips} / \mathrm{in}\). (b) Compute the
Determine all reactions and draw the shear and moment diagrams for beam \(B C\) in Figure P9.43.Assume member \(A B\) has \(2 E I\) while \(B C\) has \(E I\). 4 kips A B 18' 12'
Recompute the reactions for the frame in Figure P9.43 if support \(C\) settles 0.36 in. when the load acts and support \(A\) is constructed 0.24 in. above its intended position. Given: \(E=30,000
(a) Determine the reactions and draw the shear and moment curves for all members of the frame in Figure P9.45.Given: \(E I=\) constant. (b) Compute the vertical deflection of the girder at point
Determine the reactions at supports \(A\) and \(E\) in Figure P9.46.EI is constant for all members. B sm 100 KN C 12 m D E 8 m
Determine the reactions in the rigid frame in Figure P9.47.In addition to the applied load, the temperature of beam \(B C\) increases by \(60^{\circ} \mathrm{F}\). Given: \(I_{B C}=3600 \mathrm{in}
Determine the reactions at supports \(A\) and \(E\) in Figure P9.48.Area of bar \(E C=3\) in. \(^{2}, I_{A D}=400\) in. \({ }^{4}\), and \(A_{A D}=8\) in. \(^{2} ; E=30,000\) kips/in. \({ }^{2}\).
The tall building in Figure P9.49 is constructed of structural steel. The exterior columns, which are uninsulated, are exposed to the outside ambient temperature. To reduce the differential vertical
Using Equations 10.12 and 10.13, compute the fixed-end moments for the fixed-end beams. See Figures P10.1.Equations 10.12Equations 10.13 FEMAB A P ++ P B FEMBA
Using Equations 10.12 and 10.13, compute the fixed-end moments for the fixed-end beams. See Figures P10.2.Equations 10.12Equations 10.13 FEMAB M -- B FEMBA
Analyze by slope-deflection and draw the shear and moment curves for the beam in Figure P10.3.Given: \(E I=\) constant. 20 kips 40 kips TT B 555 40 K 40 kip. ft
Analyze the beam in Figure P10.4 by slopedeflection and draw the shear and moment diagrams for the beam. \(E I\) is constant. 24 KN 5 m A 10 m B w = 12 kN/m 14 m
Compute the reactions at \(A\) and \(C\) in Figure P10.5.Draw the shear and moment diagram for member \(B C\). Given: \(I=2000\) in. \({ }^{4}\) and \(E=3000\) kips/in. \({ }^{2}\). B +91 w = 2.8
Draw the shear and moment curves for the frame in Figure P10.6.Given: \(E I\) is constant. 10' 10' B 30 kips -14 w = 2 kips/ft + 14'-
Analyze the beam in Figure P10.7.Draw the shear and moment curves. Given: \(E=29,000 \mathrm{ksi}\) and \(I=100\) in. \({ }^{4}\). 20 kip.ft A w = 3 kips/ft B |4| 8 C D
If no vertical deflection is permitted at end \(A\) for the beam in Figure P10.8, compute the required weight \(W\) that needs to be placed at midspan of \(C D\). Given: \(E=29,000\) ksi and
(a) Under the applied loads support \(B\) in Figure P10.9 settles 0.5 in. Determine all reactions. Given: \(E=30,000 \mathrm{kips} / \mathrm{in} .^{2}\) and \(I=240 \mathrm{in} .^{4}\). (b) Compute
In Figure P10.10, support \(A\) rotates \(0.002 \mathrm{rad}\) and support \(C\) settles 0.6 in. Draw the shear and moment curves. Given: \(I=144\) in. \({ }^{4}\) and \(E=29,000\) kips/in. \({
In Problems P10.11, take advantage of symmetry to simplify the analysis by slope deflection.(a) Compute all reactions and draw the shear and moment curves for the beam in Figure P10.11.Given: \(E I\)
In Problems P10.12, take advantage of symmetry to simplify the analysis by slope deflection.(a) Determine the member end moments for the rectangular ring in Figure P10.12, and draw the shear and
In Problems P10.13, take advantage of symmetry to simplify the analysis by slope deflection.P10.13. Figure P10.13 shows the forces exerted by the soil pressure on a typical \(1-\mathrm{ft}\) length
Compute the reactions and draw the shear and moment curves for the beam in Figure P10.14.Given: \(E=\) \(200 \mathrm{GPa}\) and \(I=120 \times 10^{6} \mathrm{~mm}^{4}\). A B, w = 40 kN/m C D E
Consider the beam in Figure P10.14 without the applied load. Compute the reactions and draw the shear and moment curves for the beam if support \(C\) settles \(24 \mathrm{~mm}\) and support \(A\)
Analyze the frame in Figure P10.16.In addition to the applied loads, supports \(A\) and \(D\) settle by 2.16 in. \(E I=36,000 \mathrm{kip} \cdot \mathrm{ft}^{2}\) for beams and \(E I=72,000
Analyze the structure in Figure P10.17.In addition to the applied load, support \(A\) rotates clockwise by \(0.005 \mathrm{rad}\). Also \(E=200 \mathrm{GPa}\) and \(I=25 \times 10^{6}
Analyze the frame in Figure P10.18.Compute all reactions. Given: \(E I\) is constant. B 10% 10% 20 kips D 12'
Analyze the frame in Figure P10.19.Given: EI is constant. 6 kN/m C 50 kN 8 m 4 m -3 m D 50 kN B E 6 m
Analyze the frame in Figure P10.20.Compute all reactions. Given: \(E I\) is constant. T 10' A -10' w = 8 kips/ft + B E 10 C 15' 11.
Analyze the frame in Figure P10.20.Ignore the applied load. But support \(E\) settles by 1 in. Use \(E=\) \(29,000 \mathrm{ksi}\) and \(I=100 \mathrm{in} .^{4}\).Figure P10.20 T 10' A 10' w = 8
Compute the reactions and draw the shear and moment diagrams for beam \(B D\) in Figure P10.22.\(E I\) is constant. 35 kN 3 m 6 m C B w = 6 kN/m 9m D
Analyze the frame in Figure P10.23.Compute the reactions and draw the shear and moment diagrams for members \(A B\) and \(B D\). Given: \(E I\) is constant. A w = 5 kips/ft 15- B D 12'
If support \(A\) in Figure P10.24 is constructed 0.48 in. too low and the support at \(C\) is accidentally constructed at a slope of \(0.016 \mathrm{rad}\) clockwise from a vertical axis through

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