- Solve Prob. 7–10 using the conjugate-beam method.Data from Prob. 7–10Determine the slope at B and the maximum displacement of the beam. Use the moment-area theorems. Take E = 200 GPa, I =
- Solve Prob. F7–11 using the conjugate-beam method.Data from Prob. F7–11Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A 5 kN.m -1.5 m- C -1.5
- Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A 6 kN ↓ -1.5 m- -3 m- C -3 m- Probs. 7-12/13 B
- Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A 3 m- C 8 kN Probs. F7-13/14 3 m B
- Solve Prob. 7–12 using the conjugate-beam method.Data from Prob. 7–12:Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A 6 kN ↓ -1.5 m- -3
- Solve Prob. F7–13 using the conjugate-beam method.Data from Prob. F7–13Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A 3 m- C 8 kN Probs.
- Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A -2 m 4 kN -4 m Probs. F7-15/16 4 kN 4 m -2 m B
- Solve Prob. F7–15 using the conjugate-beam method.Data from Prob. F7–15Use the moment-area theorems and determine the slope at A and displacement at C. EI is constant. A -2 m 4 kN -4 m Probs.
- Use the moment-area theorems and determine the slope at B and displacement at B. EI is constant. A 2 m 9,kN Probs. F7-17/18 2 m B
- Solve Prob. F7–17 using the conjugate-beam method.Data from Prob. F7–17Use the moment-area theorems and determine the slope at B and displacement at B. EI is constant. A 2 m 9,kN Probs.
- Determine the slope at D and the displacement at the end A of the beam. EI is constant. Use the moment-area theorems. Moment Area Theorem. To determine tc/B we apply Theorem 2 by finding the moment
- Solve Prob. 7–18 using the conjugate-beam method.Data from Prob. 7–18Determine the slope at D and the displacement at the end A of the beam. EI is constant. Use the moment-area theorems. 7.5
- Use the moment-area theorems and determine the displacement at C and the slope of the beam at A, B, and C. EI is constant. 6 m B Prob. 7-20 -3 m C 8 kN.m
- Use the moment-area theorems and determine the slope at B and the displacement at C. The member is an A-36 steel structural Tee for which I = 76.8 in4. ...s @ 3 ft 5 k C Prob. 7-21 3 ft 1.5 k/ft B
- Determine the displacement and slope at C. EI is constant. Use the moment-area theorems. -15 ft- B -9 ft- Probs. 7-22/23 60 k-ft
- Solve Prob. 7–22 using the conjugate-beam method.Data from Prob. 7–22:Determine the displacement and slope at C. EI is constant. Use the moment-area theorems. -15 ft- B -9 ft- Probs. 7-22/23 60
- Determine the slope at B and the maximum displacement of the beam. Use the moment-area theorems. Take E = 200 GPa, I = 550(106) mm4. Moment Area Theorem. To determine tc/B we apply Theorem 2
- Solve Prob. 7–24 using the conjugate-beam method.Data from Prob. 7–24Determine the slope at B and the maximum displacement of the beam. Use the moment-area theorems. Take E = 200 GPa, I =
- The beam is subjected to the load P as shown. Use the moment-area theorems and determine the magnitude of force F that must be applied at the end of the overhang C so that the displacement at C is
- The beam is subjected to the load P as shown. If F = P, determine the displacement at D. Use the momentarea theorems. EI is constant. A P D B Probs. 7-26/27 a F C
- Use the conjugate-beam method and determine the displacement at D and the slope at C. Assume A is a fixed support and C is a roller. EI is constant. A B -L- Prob. 7-30 L P D
- Use the conjugate-beam method and determine the slope at C and the displacement at B. EI is constant. A -a с Prob.7-31 a W B
- Determine the maximum displacement of the beam and the slope at A. EI is constant. Use the moment-area theorems. 30 kN.m -6 m- Probs. 7-34/35 B
- Solve Prob. 7–34 using the conjugate-beam method.Data from Prob. 7–34:Determine the maximum displacement of the beam and the slope at A. EI is constant. Use the moment-area theorems. 30 kN.m -6
- Determine the slope to the left and right of B and the displacement at D. EI is constant. Use the moment-area theorems. A 3 m B -3 m IC Prob. 7-36 3 m 60 kN.m
- Determine the vertical displacement of joint A. Assume the members are pin connected at their end points. Take A = 3 in2 and E = 29(103) ksi for each member. Use the method of virtual work. 8 ft A 3
- Determine the displacement at C and the slope at D. Assume A is a fixed support, B is a pin, and D is a roller. Use the conjugate-beam method. DO -10 ft- |B -10 ft- Prob. 7-38 10 k C -10 ft- D
- Determine the vertical displacement of joint B. AE is constant. Use the principle of virtual work. 6 ft C 8 ft 150 lb B Probs. F8-1/2
- Solve Prob. 8–1 using Castigliano’s theorem.Data from Prob. 8–1Determine the vertical displacement of joint A. Assume the members are pin connected at their end points. Take A = 3 in2 and E =
- Solve Prob. F8–1 using Castigliano’s theorem.Data from Prob. F8–1Determine the vertical displacement of joint B. AE is constant. Use the principle of virtual work. Castigliano's Theorem.
- Determine the horizontal displacement of joint A. AE is constant. Use the principle of virtual work. A 7 kN. 2 m 60° C 2 m Probs. F8-3/4 D B
- Solve Prob. F8–3 using Castigliano’s theorem. A 7 kN. 2 m 60° C 2 m Probs. F8-3/4 D B
- Determine the horizontal displacement of joint D. AE is constant. Use the principle of virtual work. 6 kN A ID 3 m. Ic 3 m B -6 kN Probs. F8-5/6
- Solve Prob. 8–7 using Castigliano’s theorem.Data from Prob. 8–7Determine the vertical displacement of joint A. Each bar is made of steel and has the cross-sectional area shown. Take E = 29(103)
- Determine the vertical displacement of joint A. Each bar is made of steel and has the cross-sectional area shown. Take E = 29(103) ksi. Use the method of virtual work. A... 6k 2 in² 3 in² 8 ft E 3
- Solve Prob. F8–5 using Castigliano’s theorem.Data from Prob. F8–5Determine the horizontal displacement of joint D. AE is constant. Use the principle of virtual work. 6 kN A ID 3 m. Ic 3 m B -6
- Determine the vertical displacement of joint D. AE is constant. Use the principle of virtual work. 4 m -3 m- D B 50 KN Probs. F8-7/8 C
- Solve Prob. F8–7 using Castigliano’s theorem.Data from Prob. F8–7Determine the vertical displacement of joint D. AE is constant. Use the principle of virtual work. 4 m -3 m- D B 50 KN Probs.
- Use the method of virtual work and determine the vertical displacement of joint H. Each steel member has a cross-sectional area of 4.5 in2. Take E = 29(103) ksi. A 12 ft- B 6 k 12 ft- H 8 k -12
- Determine the vertical displacement of joint B. AE is constant. Use the principle of virtual work. E D B 1.5 m 1.5 m- Probs. F8-9/10 2 m C 8 kN
- Determine the reactions at the supports, then draw the moment diagram. Assume B and C are rollers and A is pinned. The support at B settles downward 30 mm. Take E = 200 GPa, I = 150(106) mm4.
- Determine the value of a so that the maximum positive moment has the same magnitude as the maximum negative moment. EI is constant. a P -L- Prob. 9-7
- Determine the reactions at the supports, then draw the shear and moment diagrams. Assume A and C are rollers and B is pinned. EI is constant. 4 m B Prob. 9-8 -4 m 60 kN-m
- Determine the force in the spring. Assume the support at A is fixed. The beam has a width of 5 mm and E = 200 GPa. A 10 mm -200 mm- Prob. 9-9 50 N B k = 2 N/mm
- Determine the reactions at the supports. Assume the support at A is fixed and B is a roller. Take E = 29(103) ksi. The moment of inertia for each segment is shown in the figure. A 2 k/ft IAB= 600 in
- Determine the reactions at the fixed supports, A and B. EI is constant. A 2 P Prob. 9-12 L 2 B.
- Determine the reactions at the supports, then draw the moment diagrams for each member. EI is constant. A 6 kN/m 3 m C Prob. 9-14 @ B 2 m -12 kN 2m
- Determine the reactions at the supports, then draw the moment diagrams for each member. Assume A and B are pins and the joint at C is fixed connected. EI is constant. 12 kN 2m 2 m 6 kN/m A 6 m Prob.
- Determine the force in each member. AE is constant. 4 kN 6 kN 4 m. Prob. 9-25 D C. B 3 m 3 m
- Determine the force in member BE. AE is constant. 3 m B E -3 m Prob. 9-29 D C 12 kN 3 m
- Determine the force in member BD. AE is constant. 12 kN D -1.5 m Probs. 9-30/31 C 9 kN 2m B
- Determine the force in member AD. AE is constant. 12 kN D A -1.5 m- Probs. 9-30/31 C 9 KN 2 m B
- Determine the reactions at the supports, then draw the moment diagram. Each spring is originally unstretched and has a stiffness k = 12 EI/L3. EI is constant. A k -L- B W Prob. 9-34 -L- C k
- The queen-post trussed beam is used to support a uniform load of 4 k/ft. Determine the force developed in each of the five struts. Neglect the thickness of the beam and assume the truss members are
- Determine the reactions at the fixed support D. EI is constant for both beams. D 3 m 30 kN B Prob. 9-39 3 m C
- The two cantilever beams are in contact using the roller support C. Determine the reactions at the fixed supports A and B when the load of 9 k is applied. EI is constant. A B -10 ft- Prob. 9-41 9 k C
- Determine the internal moments at the supports A, B, and C, then draw the moment diagram. Assume A is pinned, and B and C are rollers. EI is constant. AT -4 ft -8 ft- 3 k/ft BI -8 ft- Prob.
- Determine the moments at A, B, and C, then draw the moment diagram for the beam. Assume the supports at A and C are fixed. EI is constant. ГА -8 m- 15 KN IB 20 KN Prob. 10-5 C 4 m―4 m-
- Determine the moments at A, B, and C. The support at B settles 0.15 ft. E = 29(103) ksi and I = 8000 in4. Assume the supports at B and C are rollers and A is fixed. www. A 240 lb/ft 20 ft B Prob.
- Determine the moment at each joint of the gable frame. The roof load is transmitted to each of the purlins over simply supported sections of the roof decking. Assume the supports at A and E are pins
- The frame at the rear of the truck is made by welding pipe segments together. If the applied load is 1500 lb, determine the moments at the fixed joints B, C, D, and E. Assume the supports at A and F
- Determine the moments at each joint and fixed support, then draw the moment diagram. EI is constant. 8 k 15 ft B A 20 ft Prob. 10-23 C D doda I 10 ft
- Determine (approximately) the force in each member of the truss. Assume the diagonals cannot support a compressive force. 5 kN A -3 B 10 kN m3 m C H D- G -3 m- Probs. 12-3/4 5 KN F -3 m- E 4 m
- Determine (approximately) the force in each member of the truss. Assume the diagonals can support either a tensile or compressive force. 3 k 20 ft 4 k H -20 ft- 8 k G B -20 ft- 8 k F IC -20 ft- 4 k E
- Determine (approximately) the internal moment that member EF exerts on joint E and the internal moment that member FG exerts on joint F. 30 ft E -20 ft- F B 1.5 k/ft -30 ft- Prob. 12-13 G C -20
- Determine (approximately) the internal moments at joints A and B. F A 8m 12 kN/m E B Prob. 12-14 6 m D C
- Draw the approximate moment diagrams for each of the five girders. G H A 3 k/ft -30 ft L I B 2 k/ft -40 ft- K J C Prob. 12-15 3 k/ft T -30 ft- F E D
- Determine (approximately) the internal moments at joints E and C caused by members EF and CD, respectively. 10 ft 12 ft E 2 k/ft 3.5 k/ft 15 ft- Prob. 12-16 F D B
- Determine (approximately) the internal moments at joint H from HG and at joint J from JI and JK. I H A 5 kN/m B 3 m- J G 5 kN/m 4 m - C Prob. 12-17 K F 5 kN/m -4 m L E D
- Determine (approximately) the internal moments at joint F from FG and just below joint E on the column. F D A 2 k/ft 30 ft- 1 k/ft G E B Prob. 12-18 20 ft H C
- Determine (approximately) the internal moments at joints D and C. Assume the supports at A and B are pins. 500 lb D -10 ft- Prob. 12-19 B 12 ft il
- Determine (approximately) the internal moment and shear at the ends of each member of the portal frame. Assume the supports at A and D are (a) Pinned, (b) Fixed and (c) Partially fixed such that
- Determine the reactions at the supports. Assume ② is a roller. EI is constant. 2 1 5 kN/m 11 -2 m. 3 12 Prob. 15-1 2 -2 m 5 (3) 6
- The photo shows a structural assembly designed to support medical equipment in an operating room of a hospital. It is anticipated that this equipment weighs 1 k. Each of the side beams has a
- The concrete bridge pier, shown in the photo, supports a portion of a highway bridge. The centerline dimensions and the anticipated loading on the cap or top beam are shown in the figure. This beam
- The steel-trussed bent shown in the photo is used to support a portion of the pedestrian bridge. It is constructed using two wide-flange columns, each having a cross-sectional area of 4.44 in2 and a
- The load capacity of the historical Pratt truss shown in the photo is to be investigated when the load on the bottom girder AB is 600 lb/ft. A drawing of the bridge shows the centerline dimensions of
- The pavilion shown in the photo consists of an open roof supported by two trussed frames. Each of these frames consists of members CD and DE that have a cross-sectional area of 8.08(10 - 3) m2 and a
- Ifdetermine 2A + B and 4A - B. A 2 5 -1 3 = [₁ 0 =[2 and B = 8
- Ifdetermine 2A + B and 4A - B. A [4 5 -3] 6 1 2 and B · [ -4 6 0 2 0 10
- A = [-4 -3], anddetermine AB. B = 2 5 3 -1
- If A = [6 2 3] and B = [1 6 4], show that (A + B)T = AT + BT.
- Ifdetermine A + AT. A 2 -2 [₁ 5 9
- Ifdetermine A AT. A 4 -2 1- 5 3
- Ifdetermine A AT. A || 4 6 1 1 2 0 3 -1 2
- Ifdetermine A B. A = 6 2 0 4 2 1 1 1 -3 and B = -1 3 -2 2 4 1 07 5
- Ifdetermine A B. A = [₁ 2 -2 73 1 0 and B = [
- Ifdetermine B A. A = 4 5 1 -1 1 2 24 2 and B = -2 4 1 20 2 14 1
- Show that the distributive law is valid, i.e., A(B + C) = AB AC, if A = 3 2 2 |--[-]-[] B = -2, C = 4 4 -4 8 6 2 2
- Show that the associative law is valid, i.e., A(BC) = 3 -4 8 6 2 (AB)C, if A = A = [2 B= 2 -2, C = [2 4 -6]. 4
- Evaluate the determinants 3 2 6 5 and 24 68 2 5 4 -1 3
- Ifdetermine A-1. A || = 2 2 0 8 6 3 1 1 -3
- If determine A -1. A = [3³₁ [5 2 -4.
- Solve the equations 2x1 - 2x2 + 2x3 = -2, -2x1 + 2x2 + 2x3 = -2, and 2x1 + 4x2 - 4x3 = 10, using the matrix equation x = A-1C.
- Solve the equations in Prob. A–18 using the Gauss elimination method.Data from Prob. A–18Solve the equations 2x1 - 2x2 + 2x3 = -2, -2x1 + 2x2 + 2x3 = -2, and 2x1 + 4x2 - 4x3 = 10, using the
- Solve the equations x1 + 4x2 + x3 = -1, 2x1 - x2 + x3 = 2, and 4x1 - 5x2 + 3x3 = 4, using the matrix equation x = A-1C.
- Solve Prob. 8–9 using Castigliano’s theorem.Data from Prob. 8–9Use the method of virtual work and determine the vertical displacement of joint H. Each steel member has a cross-sectional area of
- Solve the equations in Prob. A–20 using the Gauss elimination method.Data from Prob. A–20Solve the equations x1 + 4x2 + x3 = -1, 2x1 - x2 + x3 = 2, and 4x1 - 5x2 + 3x3 = 4, using the matrix
- Solve Prob. F8–9 using Castigliano’s theorem.Data from Prob. F8–9Determine the vertical displacement of joint B. AE is constant. Use the principle of virtual work. E D B 1.5 m 1.5 m- Probs.
- Determine the horizontal displacement of joint A of the truss. Each member has a cross-sectional area of A = 300 mm2, E = 200 GPa. Use the method of virtual work. B D -4 m Ela 3 m C - 30 kN 3