Questions and Answers of Structural Analysis

Determine the horizontal and vertical displacements at joint (3) of the assembly in Prob. 14-1.Data From Problem 14.1 3ft 3 ft 6 2 00 (3) 4 k +3 1 4 ft 6 ft
Determine the force in each member of the assembly in Prob. 14-1.Data From Problem 14.1 3 ft 3 ft 5 4'k 1 4. 3 -4 ft- 6 ft-
Determine the internal loadings at the ends of each member. Take \(E=29\left(10^{3}\right) \mathrm{ksi}, I=700 \mathrm{in}^{4}, A=30 \mathrm{in}^{2}\) for each member. 12 ft (1) 5 3 6 ft- 8 k 2 6 ft
Determine the rotation at (1) and (3) and the support reactions. Take \(E=29\left(10^{3}\right) \mathrm{ksi}, I=600 \mathrm{in}^{4}, A=10 \mathrm{in}^{2}\) for each member. Assume joints (1) and (3)
Determine the reactions at the pinned supports (1) and (4). Joints (2) and (3) are fixed connected. Take \(E=29\left(10^{3}\right) \mathrm{ksi}, I=\) \(700 \mathrm{in}^{4}, A=15 \mathrm{in}^{2}\) for
Determine the structure stiffness matrix \(\mathbf{k}\) for each member of the two-member frame. Take \(E=200 \mathrm{GPa}, I=350\left(10^{6}\right) \mathrm{mm}^{4}\), \(A=20\left(10^{3}\right)
Determine the support reactions at (1) and (3). Take \(E=200 \mathrm{GPa}, I=350\left(10^{6}\right) \mathrm{mm}^{4}, A=20\left(10^{3}\right) \mathrm{mm}^{2}\) for each member. Supports (1) and (3)
Determine the horizontal and vertical shear acting in panels \(C\) and \(D\) of the building when the wind acts on the adjacent walls of the building. 1.2 kPa 30 m 20 m 4 m 4 m CA DB 3 m 0.8 kPa (a)
Solve Prob. 13-1 using the slope-deflection equations.Data From Problem 13.1 4 ft 2 ft B 8 k/ft ft 4 t 6 ft- 4 ft 4 ft. -6 ft 20 ft 20 ft
Solve Prob. 13-3 using the slope-deflection equations.Data From Problem 13.3 4 ft 2 ft 40 ft 8 ft- 2 ft 1.5 k/ft 40 ft 12 ft B 15 ft
Solve Prob. 13-5 using the slope-deflection equations.Data From Problem 13.5 4 It 6 ft 2 ft 4 ft 4 k/ft D B 9 ft 8 ft 25 ft 2 ft E 30 ft- 40 ft 30 ft.
Solve Prob. 13-7 using the slope-deflection equations.Data From Problem 13.7 2 ft 2 k/ft 5 ft B 2 ft 3 ft- 9 ft. 3 ft- -2 ft 5 ft
Solve Prob. 13-9 using the slope-deflection equations.Data From Problem 13.9 500 lb/ft 2.5 T 2.5 ft 1 ft 6 ft- 18 ft 6 ft- 1 ft 1 ft- 20 ft A
Solve Prob. 13-11 using the slope-deflection equations.Data From Problem 13.11 40 ft 40 ft 40 ft 2 k/ft 3 ft B 3 ft 12 ft 2 ft 12 ft 4 ft 30 ft
Determine the moments at the ends of each member of the frame. The members are fixed connected at the supports and joints. \(E I\) is the same for each member. 20 k B 4 k/ft 6 ft 15 ft 15k- 6 ft D A
Determine the horizontal and vertical components of reaction at the pin supports \(A\) and \(D\). EI is constant. 12 ft. A B 10 k 5 ft 8 ft 2 ft -5 ft- D
Solve Prob. 12-1 assuming that the diagonals cannot support a compressive force.Data From Problem 12.1 3 m 50 kN 40 kN 20 kN F 3 m B 3 m + D C
Solve Prob. 12-3 assuming that the diagonals cannot support a compressive force.Data From Problem 12.3 A 2 m E 2 m D 1.5 m B 4 kN 8 kN
Solve Prob. 12-5 assuming that the diagonals cannot support a compressive force.Data From Problem 12.5 6 ft A 7 k 14 k 14 k 7 k H E 2 k 8 ft B C 8 ft 8 ft D
Determine (approximately) the moments at joint \(K\) from \(J K\) and at fixed support \(B\). 30 kN/m 20 kN/m 20 kN/m 1. K 40 kN/m 20 kN/m 20 kN/m H A G F B 6 m 6 m 6 m E D
Solve Prob. 12-21 if the supports at \(A\) and \(B\) are pinned instead of fixed.Data From Problem 12.21 12 kN 1.5 m, 1.5 m. 3 m E 8 kN G H I C A -3 m -3 m. B 2 m 6 m
Solve Prob. 12-23 if the supports at \(A\) and \(B\) are fixed instead of pinned.Data From 12.23 8 k T 5 ft E -5 ft- 7 ft A -5 ft- F H G 5 ft 20 ft B
Solve Prob. 12-25 if the supports at \(A\) and \(B\) are fixed instead of pinned.Data From Problem 12.25 20 k 10 k 8 ft E 10 ft H 15 ft C 000066. 10 ft- F 4 ft 1 4 ft D A Bo
Solve Prob. 12-28 if the supports at \(A\) and \(B\) are fixed instead of pinned.Data From Problem 12.28 500 lb E 1.5 ft 6 ft 1.5 ft 7 ft H 1.5 ft
Solve Prob. \(12-30\) if the supports at \(A\) and \(B\) are fixed instead of pinned.Data From Problem 12.30 4 k 6 ft 6 ft K 3 ft E H C L 12 ft B 8 ft 8 ft 8 ft 8 ft
Solve Prob. 12-32 if the supports at A and B are fixed instead of pinned.Data From Problem 12.32 6@ 1.5 m 9m H G 2 kN 4 kN J K L M N O C B D 1.5 m 1 m 4 m
Draw (approximately) the moment diagram for the girder \(E F G H\). Use the portal method. 36 kN E F G H 10 m. B 8m+ C -12 m- 8 m D
Draw the moment diagram for girder \(I J K L\) of the building frame. Use the cantilever method of analysis. All columns have the same cross-sectional area. 20 kN- E 35 kN- kN- F H 4 m 4 m D A B -4 m
Draw (approximately) the moment diagram for the girder \(E F G H\). Use the portal method. 24 k * 15 ft E F A B 15 ft + -30 ft C 15 ft H D
Draw the moment diagram for girder \(I J K L\) of the building frame. Use the cantilever method of analysis. Each column has the cross-sectional area indicated. J K L 20 kN 40 kN E F A I 4 m B + I 2
Determine the slope at \(C\) and the deflection at \(B\) of the bar in Prob. \(7-2\).Data From Problem 7.2 8 ft 200 lb. C -8 ft + B
Determine the elastic curve for the cantilevered W14 \(\times 30\) beam using the \(x\) coordinate. Specify the maximum slope and maximum deflection. Take \(E=29\left(10^{3}\right)\) ksi. A x 9 ft 3
Determine the maximum deflection of the beam and the slope at \(A\). \(E I\) is constant. A |- Mo Mo a B
Solve Prob. 7-10 using the conjugate-beam method.Data From Problem 7.10 |- A 2 m 30 kN B 1 m
Solve Prob. 7-12 using the conjugate-beam method.Data From Problem 7.12 A P a B a C
Solve Prob. 7-14 using the conjugate-beam method.Data From Problem 7.14 P A a+ D L 2 P 12 B
Solve Prob. 7-16 using the conjugate-beam method.Data From Problem 7.16 P a+ D L P 2 2 B
Solve Prob. 7-18 using the conjugate-beam method.Data From 7.18 A 30 ft B 15 ft- 15 k C
Solve Prob. 7-22 using the conjugate-beam method.Data From Problem 7.22 4 kN B 3 m 1.5 m 1.5 m 3 m 4 kN C
Solve Prob. 7-28 using the conjugate-beam method.Data From Problem 7.28 12 k.ft A 6 k B C 4 ft 6 ft
Solve Prob. 7-34 using the moment-area theorems.Data From Problem 7.34 A 36 k-ft B -9 ft- -9 ft- ft- -9 ft 15 k
Solve Prob. 7-36 using the conjugate-beam method.Data From Problem 7.36 A 6 ft B I 6 ft + 6 ft- 60 k-ft D
Solve Prob. 8-5 using Castigliano's theorem.Data From Problem 8.5 A F E B 45 kN. 2 m +-+- 2 m - D 1.5 m
Solve Prob. 8-7 using Castigliano's theorem.Data From Problem 8.7 A + 4 m D DDD CC B 15 kN 4 m E 00 6% 00 [006 C 3 m 20 kN
Solve Prob. 8-11 using Castigliano's theorem.Data From Problem 8.11 A -4m B H C D 4 m 4 m 4 m 3 kN 3 kN 4 kN 3 m E
Solve Prob. 8-13 using Castigliano's theorem.Data From Problem 8.13 Use the method of virtual work and determine the horizontal displacement of point C. Each steel member has a cross-sectional area
Solve Prob. 8-19 using Castigliano's theorem.Data From Problem 8.19 A 6 k 6 ft 6 ft 12 k-ft.
Solve Prob. 8-23 using Castigliano's theorem.Data From Problem 8.23 a B a P C
Solve Prob. 8-27 using Castigliano's theorem.Data From Problem 8.27 A 300 N/m 400 N 3 m B
Solve Prob. 8-29 using Castigliano's theorem.Data From Problem 8.29 A 3 m B 6 kN/m 3 m C
Solve Prob. 8-31 using Castigliano's theorem.Data From Problem 8.31 C L B L W
Solve Prob. 8-33 using Castigliano's theorem.Data From Problem 8.33 A 2 k/ft 12 ft B 6 ft C
Beam \(A B\) has a square cross section of \(100 \mathrm{~mm}\) by \(100 \mathrm{~mm}\). Bar \(C D\) has a diameter of \(10 \mathrm{~mm}\). If both members are made of A992 steel, determine the
Beam \(A B\) has a square cross section of \(100 \mathrm{~mm}\) by \(100 \mathrm{~mm}\). Bar \(C D\) has a diameter of \(10 \mathrm{~mm}\). If both members are made of A992 steel, determine the slope
Solve Prob. 8-37 using Castigliano's theorem.Data From Problem 8.37 A 2m B 16 kN/m 4 m
Solve Prob. 8-40 using Castigliano's theorem.Data From Problem 8.40 2 k/ft 8 ft 8 ft B
Solve Prob. \(8-48\), including the effect of shear and axial strain energy.Data From Problem 8.48 = ABC 6.5(103) mm = = IBC 100(106) mm* AAB - 18(103) mm = TAR 400(10) mm A 3 m B -50 kN 1 m
Solve Prob. 8-48 using Castigliano's theorem.Data From Problem 8.48 = ABC 6.5(103) mm IBC 100(10) mm+ AAB = 18(10) mm IAR 400(10) mm+ DA = 3 m B -50 kN 1 m
Determine the horizontal displacement at \(C\). Take \(E=29\left(10^{3}\right) \mathrm{ksi}, I=150 \mathrm{in}^{4}\) for each member. Use the method of virtual work. 8k- C 8 ft 10 ft D B
Solve Prob. 8-53 using Castigliano's theorem.Data From Problem 8.53 8 k 10 ft. 8 ft D A B
Determine the horizontal displacement of the rocker at \(B\). Take \(E=29\left(10^{3}\right) \mathrm{ksi}, I=150 \mathrm{in}^{4}\) for each member. Use the method of virtual work. 8k- C 8 ft 10 ft B
Solve Prob. 8-55 using Castigliano's theorem.Data From Problem 8.55 8 k 8 ft 10 ft D A B
Solve Prob. 8-57 using Castigliano's theorem.Data From Problem 8.57 B. 2 k 1 in 5 k 4 ft 2 in2 1 in 2in2 3 ft-
The bent rod has an \(E=200 \mathrm{GPa}, G=75 \mathrm{GPa}\), and a radius of \(30 \mathrm{~mm}\). Use Castigliano's theorem and determine the vertical deflection at \(C\). Include the effects of
Solve Prob. 8-63 using Castigliano's theorem.Data From Problem 8.63 2 L 'B- L A
The beam is supported by a pin at \(A\), a spring having a stiffness \(k\) at \(B\), and a roller at \(C\). Determine the force the spring exerts on the beam. \(E I\) is constant. L B L W C
Sketch the influence line for the shear at \(B\). If a uniform live load of \(6 \mathrm{kN} / \mathrm{m}\) is placed on the beam, determine the maximum positive shear at \(B\). Assume the beam is
Sketch the influence line for the moment at \(B\). If a uniform live load of \(6 \mathrm{kN} / \mathrm{m}\) is placed on the beam, determine the maximum positive moment at \(B\). Assume the beam is
Draw the influence line for the reaction at point \(A\). Plot numerical values every \(5 \mathrm{ft}\). Assume the support at \(A\) is a roller and \(C\) is fixed. \(E I\) is constant. 10 ft B 10 ft-
Determine the forces \(\mathbf{P}_{1}\) and \(\mathbf{P}_{2}\) needed to hold the cable in the position shown, i.e., so segment \(B C\) remains horizontal. A D E B 8 kN P 4 m 5 m 1.5 m 4 m 2 m 3 m
The cable is subjected to the uniform loading. Determine the equation \(y=f(x)\) which defines the cable shape \(A B\) and the maximum tension in the cable.. 50 ft 50 ft |- B 150 lb/ft 20 ft x
The beams \(A B\) and \(B C\) are supported by the cable that has a parabolic shape. Draw the shear and moment diagrams for members \(A B\) and \(B C\). The hanger at \(B\) is attached to member \(A
The cable has a mass of \(0.5 \mathrm{~kg} / \mathrm{m}\) and is \(25 \mathrm{~m}\) long. Determine the vertical and horizontal components of force it exerts on the top of the tower. B 30 15 m
The \(10-\mathrm{kg} / \mathrm{m}\) cable is suspended between the supports \(A\) and \(B\). If the cable can sustain a maximum tension of \(1.5 \mathrm{kN}\) and the maximum sag is \(3
A cable has a weight of \(3 \mathrm{lb} / \mathrm{ft}\) and is supported at points that are \(500 \mathrm{ft}\) apart and at the same elevation. If it has a length of \(600 \mathrm{ft}\), determine
The cable has a weight of \(5 \mathrm{lb} / \mathrm{ft}\). If it can \(\operatorname{span} L=300 \mathrm{ft}\) and has a sag of \(h=15 \mathrm{ft}\), determine the length of the cable. The ends \(A\)
Solve Prob. 6-1 using the Müller-Breslau principle.Data From Problem 6.1 3 ft 6 ft C 6 ft B 9 ft
Solve Prob. 6-3 using the Müller-Breslau principle.Data From Problem 6.3 A B 2 m 1 m
Solve Prob. 6-5 using the Müller-Breslau principle.Data From Problem 6.5 B 5 ft 5 ft A
Solve Prob. 6-7 using the Müller-Breslau principle.Data From Problem 6.7 A C 4 m 8 m
Solve Prob. 6-9 using Müller-Breslau’s principle.Data From Problem 6.9 B C 6 fl 6 ft 3 ft 3 ft
Solve Prob. 6-11 using Muller-Breslau's principle.Data From Problem 6.11 A -10 ft- C -10 ft- B 10 ft D
Solve Prob. 6-13 using the Müller-Breslau principle.Data From Problem 6.13 C B 2 m 2 m 2 m 2 m
Draw the influence line for the shear within panel \(C D\) and for the moment at \(E\) in the girder. Determine(a) the maximum shear in panel \(C D\) (b) the maximum moment in the girder at \(E\) if
A uniform live load of \(300 \mathrm{lb} / \mathrm{ft}\) and a single concentrated live force of \(2 \mathrm{k}\) are to be placed on the floor beams. Determine (a) the maximum negative shear in
A uniform live load of \(0.2 \mathrm{k} / \mathrm{ft}\) and a single concentrated live force of \(4 \mathrm{k}\) are to be placed on the floor slabs. Determine (a) the maximum live vertical reaction
Draw the influence line for the force in member \(R Q\) of the Baltimore truss. W TSRQ P N BCDEFGHIJKL 12 @25 ft - 300 ft 25 ft 25 ft M
Draw the influence line for the force in member \(N P\) of the Baltimore truss. TSRQ P B CDEFGHI 12 @25 ft 300 ft = 25 ft 25 ft M J K L
Draw the influence line for the force in member \(R N\) of the Baltimore truss. TSRQ P X X X Y X X BCDEFGHIJKL 12 @25 ft - 300 ft M 25 ft 25 ft
Draw the influence line for the force in member \(N G\) of the Baltimore truss. TSRQ P V BCDEFGHIJKL 12 @25 ft 300 ft 25 ft 25 ft M
Draw the influence line for the force in member \(C O\) of the Baltimore truss TSRQ P 25 ft W 25 ft M B C D E F G H I J K L 12 @25 ft = 300 ft
The roof truss serves to support a crane rail which is attached to the bottom cord of the truss as shown. Determine the maximum force (tension or compression) that can be developed in member \(G F\),
The truck and trailer exerts the wheel reactions shown on the deck of the girder bridge. Determine the largest moment it exerts in the splice at \(C\). Assume the truck travels left to right along
The car has a weight of \(4200 \mathrm{lb}\) and a center of gravity at \(G\). Determine the maximum moment created in the side girder at \(C\) as it crosses the bridge. Assume the car can travel in
Determine the distance \(a\) of the overhang of the beam in order that the moving loads produce the same maximum moment in magnitude at the supports as in the center of the span. Assume \(A\) is a
The maximum wheel loadings for the wheels of a crane that is used in an industrial building are given. The crane travels along the runway girders that are simply supported on columns. Determine (a)
The beam \(A B\) will fail if the maximum internal moment at \(D\) reaches \(4.50 \mathrm{kN} \cdot \mathrm{m}\) or the normal force in member \(B C\) becomes \(6 \mathrm{kN}\). Determine the largest
The flooring system for a building consists of a girder that supports laterally running floor beams, which in turn support the longitudinal simply supported floor slabs. Draw the shear and moment
The concrete beam supports the wall, which subjects the beam to the uniform loading shown. The beam itself has cross-sectional dimensions of 12 in. by 26 in. and is made from concrete having a
Leg \(B C\) on the framework can be designed to extend either outward as shown, or inward with the support \(C\) positioned below the center 2-k load. Draw the moment diagrams for the frame in each

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