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engineering
structural analysis

Structural Analysis 10th Edition Russell Hibbeler - Solutions

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 matrix equation x = A-1C.
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 4.5 in2. Take E = 29(103) ksi. A 12 ft- B 6 k 12 ft- H 8 k -12 ft. Probs. 8-9/10 G D 6 k -12
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 equation x = A-1C.
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. F8-9/10 2 m C 8 kN
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 m Probs. 8-11/12 60 KN
Determine the vertical displacement of joint C. AE is constant. Use the principle of virtual work. A -2m- H B 30 kN 2 m G 4000 C -2m- 40 kN F Probs. F8-11/12 D -2m- 30 kN 2 m E
Solve Prob. 8–11 using Castigliano’s theorem.Data from Prob. 8–11Determine 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 m Probs. 8-11/12 60 KN
Solve Prob. F8–11 using Castigliano’s theorem.Data from Prob. F8–11Determine the vertical displacement of joint C. AE is constant. Use the principle of virtual work. A -2m- H B 30 kN 2 m G 4000 C -2m- 40 kN F Probs. F8-11/12 D -2m- 30 kN 2 m E
Determine the vertical displacement of point A. Assume the members are pin connected at their ends. Take A = 100 mm2 and E = 200 GPa for each member. Use the method of virtual work. 10:00 tal TON 1000 90000003 450. 9000 20 KN 4 m E (₂) B 190 good jeo e o oc 40 kN 4 m Probs. 8-13/14 Doodl 20 kN 3 m
Determine the slope and displacement at point A. EI is constant. Use the principle of virtual work. 30 kN -3 m Probs. F8-13/14 B
Solve Prob. 8–13 using Castigliano’s theorem.Data from Prob. 8–13Determine the vertical displacement of point A. Assume the members are pin connected at their ends. Take A = 100 mm2 and E = 200 GPa for each member. Use the method of virtual work. Castigliano's Theorem. Setting P = 20 kN, its
Solve Prob. F8–13 using Castigliano’s theorem.Data from Prob. F8–13Determine the slope and displacement at point A. EI is constant. Use the principle of virtual work. 30 kN -3 m Probs. F8-13/14 B
Determine the vertical displacement of joint C. Assume the members are pin connected at their end points. Take A = 200 mm2 and E = 200 GPa for each member. Use the method of virtual work. 4 m A E 4 m 24 kN B D Probs. 8-15/16 4 m 12 kN C
Determine the slope and displacement at point A. EI is constant. Use the principle of virtual work. 4 kN.m A 3 m Probs. F8-15/16 B
Solve Prob. 8–15 using Castigliano’s theorem.Data from Prob. 8–15Determine the vertical displacement of joint C. Assume the members are pin connected at their end points. Take A = 200 mm2 and E = 200 GPa for each member. Use the method of virtual work. Castigliano's Theorem. Setting P = 20
Solve Prob. F8–15 using Castigliano’s theorem.Data from Prob. F8–15Determine the slope and displacement at point A. EI is constant. Use the principle of virtual work. 4 kN.m A 3 m Probs. F8-15/16 B
Determine the vertical displacement of joint C if members AB and BC experience a temperature increase of δT = 50C. Take a = 12(10 - 6)/°C. 4 m A E -4m- B D Probs. 8-17/18 4 m C
Determine the slope and displacement at point B. EI is constant. Use the principle of virtual work. A 18 kN/m 3 m Probs. F8-17/18 B
Determine the vertical displacement of joint C if member CD is fabricated 10 mm too long. 4 m A E -4m- B D Probs. 8-17/18 4 m C
Solve Prob. F8–17 using Castigliano’s theorem.Data from Prob. F8–17Determine the slope and displacement at point B. EI is constant. Use the principle of virtual work. A 18 kN/m 3 m Probs. F8-17/18 B
Determine the slope at A and displacement at point C. EI is constant. Use the principle of virtual work. 4m C 8 kN/m न Probs. F8-19/20 4m B
Solve Prob. 8–19 using Castigliano’s theorem.Data from Prob. 8–19Determine the displacement of point C and the slope at point B. EI is constant. Use the principle of virtual work. L 2 C Probs. 8-19/20 를 LG CO B S
Solve Prob. F8–19 using Castigliano’s theorem.Data from Prob. F8–19Determine the slope at A and displacement at point C. EI is constant. Use the principle of virtual work. 4m C 8 kN/m न Probs. F8-19/20 4m B
Determine the slope and displacement at point C. EI is constant. Use the principle of virtual work. 12 kN A -2 m C Probs. F8-21/22 -2 m B
Determine the slope and displacement at point C. Use the principle of virtual work. EI is constant. 2 m C 1 m- 12 kN/m Probs. 8-21/22 3 m B
Solve Prob. 8–21 using Castigliano’s theorem.Data from Prob. 8–21Determine the slope and displacement at point C. Use the principle of virtual work. EI is constant. 2 m C 1 m- 12 kN/m Probs. 8-21/22 3 m B
Solve Prob. F8–21 using Castigliano’s theorem.Data from Prob. F8–21Determine the slope and displacement at point C. EI is constant. Use the principle of virtual work. Castigliano's Theorem. Setting P = 20 kN, its actual value, and applying Eq. 8-28, 3 kN Ac 3 kN ↓ = = = |x₁|1₁ - 2
Determine the displacement at point C. EI is constant. Use the principle of virtual work. A 6 m C Probs. F8-23/24 -6 m- 12 kN/m B
Determine the slope and displacement at the end A of the beam. Take E = 29(103) ksi, I = 170 in4. Use the method of virtual work. A 2 k/ft -10 ft- B -10 ft- 10 k Probs. 8-24/25 -10 ft
Solve Prob. F8–23 using Castigliano’s theorem.Data from Prob. F8–23Determine the displacement at point C. EI is constant. Use the principle of virtual work. A 6 m C Probs. F8-23/24 -6 m- 12 kN/m B
Solve Prob. 8–24 using Castigliano’s theorem.Data from Prob. 8–24Determine the slope and displacement at the end A of the beam. Take E = 29(103) ksi, I = 170 in4. Use the method of virtual work. Castigliano's Theorem. Setting P = 20 kN, its actual value, and applying Eq. 8-28, 3 kN Ac 3
Determine the displacement and slope at point C of the cantilever beam. The moment of inertia of each segment is indicated in the figure. Take E = 200 GPa. Use the principle of virtual work. A 12 kN/m LAB = 600 (106) mm4 2m Probs. 8-26/27 8 kN/m C BIBC = 150 (106) mm 4 1 m
Solve Prob. 8–26 using Castigliano’s theorem.Data from Prob. 8–26Determine the displacement and slope at point C of the cantilever beam. The moment of inertia of each segment is indicated in the figure. Take E = 200 GPa. Use the principle of virtual work. A 12 kN/m LAB = 600 (106)
Solve Prob. 8–28 using Castigliano’s theorem.Data from Prob. 8–28Determine the slope at A. EI is constant. Castigliano's Theorem. Setting P = 20 kN, its actual value, and applying Eq. 8-28, 3 kN Ac 3 kN ↓ = = = |x₁|1₁ - 2 m 0 M₁ M ¹(34x₁4x1)(0.5x₁1) dx₁ *(18x2)(0.5x₂)
Determine the slope at A. EI is constant. C - L B Probs. 8-28/29 L- W
Determine the slope and displacement at point C. EI is constant. Assume A is a pin. Use the method of virtual work. A 2 k/ft 12 ft B Probs. 8-30/31 6 ft C
Solve Prob. 8–30 using Castigliano’s theorem.Data from Prob. 8–30Determine the slope and displacement at point C. EI is constant. Assume A is a pin. Use the method of virtual work. Castigliano's Theorem. Setting P = 20 kN, its actual value, and applying Eq. 8-28, 3 kN Ac 3
Bar ABC has a rectangular cross section of 300 mm by 100 mm. Attached rod DB has a diameter of 20 mm. Determine the vertical displacement of point C due to the loading. Consider only the effect of bending in ABC and axial force in DB. E = 200 GPa. VE-aust A H 100 mm 300 mm 3m B 3 m Probs.
Bar ABC has a rectangular cross section of 300 mm by 100 mm. Attached rod DB has a diameter of 20 mm. Determine the slope at A due to the loading. Consider only the effect of bending in ABC and axial force in DB. E = 200 GPa. VE-aust A 4 300 mm 100 mm 3m B 3 m Probs. 8-32/33 D PARIS 2 20 KN 4 m
Determine the slope and displacement at point B. Assume the support at A is a pin and C is a roller. Take E = 200 GPa, I = 150(106) mm4. Use the method of virtual work. A -2 m 16 kN/m B 4 m Probs. 8-34/35/36 C
Solve Prob. 8–34 using Castigliano’s theorem.Data from Prob. 8–34Determine the slope and displacement at point B. Assume the support at A is a pin and C is a roller. Take E = 200 GPa, I = 150(106) mm4. Use the method of virtual work. A -2 m 16 kN/m B 4 m Probs. 8-34/35/36 C
Determine the slope and displacement at point B. Assume the support at A is a pin and C is a roller. Account for the additional strain energy due to shear if the cross section is a wide flange. Take E = 200 GPa, I = 150(106) mm4, G = 75 GPa, and assume AC has a cross-sectional web area of A =
Determine the reactions at the fixed support at A and the roller at B. EI is constant. A -2m- B Prob. F9-1 -2 m 40 kN
Determine the reactions at the supports, then draw the shear and moment diagrams. Assume the support at A is fixed and B is a roller. EI is constant. 500 lb/ft A -12 ft- Prob. 9-1 'В
Determine the reactions at the fixed support at A and the roller at B. EI is constant. A PERCORRE Wo - L Prob. F9-2 B
Determine the reactions at the fixed support at A and the roller at B. Support B settles 5 mm. Take E = 200 GPa and I = 300(106) mm4. A 10 kN/m 6 m Prob. F9-3 B
Determine the reactions at the pin at A and the rollers at B and C. EI is constant. Mo A L B Prob. F9-4 L C
Determine the support reactions. Assume B is a pin and A and C are rollers. EI is constant. A 4 kN/m 15 m- B Prob. 9-4 -20 m C
Determine the reactions at the pin A and the rollers at B and C on the beam. EI is constant. A -2 m 50 KN B- -2 m Prob. F9-5 4 m C
Determine the reactions at the supports, then draw the moment diagram. The moment of inertia for each segment is shown in the figure. Assume A and C are rollers and B is a pin. Take E = 200 GPa. 20 KN 20 kN 40 kN LAB = 120(106) mm4B IBC = 90(106) mm IC |3m|3m|3m- -4m4 -4 m Prob. 9-5 m
Determine the reactions at the pin at A and the rollers at B and C on the beam. Support B settles 5 mm. Take E = 200 GPa, I = 300(106) mm4. 6 m 10 kN/m B Prob. F9-6 6 m
Draw the shear and moment diagrams for the beam. Indicate values at the supports and at the points where a change in load occurs. 6 kN/m A -2 m- -2 m- Prob. F4-19 6 kN/m B -2 m-
Use 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 m- Probs. F7-11/12 B
Draw the moment diagrams for the frame. Assume the frame is pin connected at A, B, and C and fixed connected at E and D. 30 kN 6 m -3 m- -2 m B A C -2 m D E Prob. F4-22 2 kN/m
Determine the horizontal and vertical components of reaction at pins A, B, and C of the two-member frame. A 300 lb B |--2 ft2 ft- Prob. F2-5 4 ft C 3 ft
Determine the force in members HG, BG, and BC and state whether they are in tension or compression. A -5 ft 2 k H B -5 ft- 2 k G C -5 ft- Prob. F3-7 2 k 00 D -5 ft- E 5 ft
The wall is 15 ft high and consists of 2 * 4 in. studs, plastered on one side. On the other side there is 4-in. clay brick. Determine the average load in lb/ft of length of wall that the wall exerts on the floor. Prob. 1-2
The precast floor beam is made from concrete having a specific weight of 23.6 kN/m3. If it is to be used for a floor of an office building, calculate its dead and live loadings per foot length of beam. 0.15 m 0.3 m ↓ 1.5 m. H 0.15 m Prob. 1-5
A building wall consists of 12-in. clay brick and 1/2 -in. fiberboard on one side. If the wall is 10 ft high, determine the load in pounds per foot that it exerts on the floor.
The precast inverted T-beam has the cross section shown. Determine its weight per foot of length if it is made from reinforced stone concrete and twelve 34 -in.-diameter cold-formed steel reinforcing rods. 36 in. 12 in. 1 9 00 in., 00 000000 48 in. Prob. 1-7
The hollow core panel is made from plain stone concrete. Determine the dead weight of the panel. The holes each have a diameter of 4 in. 7 in. 12 in12 in-12 in-12 in. 1-12 in 12 in. Prob. 1-8 12 ft
The floor of a light storage warehouse is made of 6-in.-thick cinder concrete. If the floor is a slab having a length of 10 ft and width of 8 ft, determine the resultant force caused by the dead load and that caused by the live load.
Wind blows on the side of a fully enclosed 30-ft-high hospital located on open flat terrain where V = 120 mi/h. Determine the design wind pressure acting over the windward wall of the building at the heights 0–15 ft, 20 ft, and 30 ft. The roof is flat. Take Ke = 1.0. 1 1006 01 Prob. 1-16 314
A hospital located in Chicago, Illinois, where the ground snow load is 25 lb/ft2, has a flat roof. Determine the design snow load on the roof of the hospital.
Determine the resultant force acting on the face of the sign if qh = 25.5 lb/ft2. The sign has a width of 32 ft and a height of 8 ft as indicated. 32 ft. Prob. 1-19 8 ft 8 ft
The barn has a roof with a slope of 40 mm/m. It is located in an open field where the ground snow load is 1.50 kN/m2. Determine the snow load that is required to design the roof of the stall.
The stall has a flat roof with a slope of 40 mm/m. It is located in an open field where the ground snow load is 0.84 kN/m2. Determine the snow load that is required to design the roof of the stall. Prob. 1-21
Determine the horizontal and vertical components of reaction at the pins A, B, and C. 3 m A C -2m- 3 kN/m Prob. F2-1 -2 m B
Determine the horizontal and vertical components of reaction at the pins A, B, and C. A 10 kN/m - 4 m- Prob. F2-2 B 45° 2 m C
Determine the horizontal and vertical components of reaction at the pins A, B, and C. A 10 kN/m -2m- -2m- Prob. F2-3 B 60° C
Determine the horizontal and vertical components of reaction at the roller support A, and fixed support B. A -1 m- 10 kN 4 m Prob. F2-4 8 kN/m -2 m- B
Determine the components of reaction at the roller support A and pin support C. Joint B is fixed connected. on A -2 m- 6 kN -2 m- B C Prob. F2-6 2 m 2 m 2 kN
Determine the horizontal and vertical components of reaction at the pins A, B, and D of the three-member frame. The joint at C is fixed connected. 3 kN/m -3 m B -2 m 8 kN -2 m Prob. F2-7 8 kN N C D 4 m
Determine the components of reaction at the fixed support D and the pins A, B, and C of the three-member frame. Neglect the thickness of the members. 4 kN. T 3 m 3 m B A 2 m 6 kN -2 m Prob. F2-8 6 kN -2 m C D
Determine the components of reaction at the fixed support D and the pins A, B, and C of the three-member frame. Neglect the thickness of the members. 0.5 k/ft B A 2 k/ft 8 ft Prob. F2-9 C D 4 ft 2 ft
Determine the components of reaction at the fixed support D and the pins A, B, and C of the three-member frame. Neglect the thickness of the members. 6 m 6 kN 18 B -2 m- B 8 kN A 8 kN -2 m- I 6 kN Prob. F2-10 -2 m- TH C D 1.5 kN/m
Determine the force in each member of the truss and state whether it is in tension or compression. 3 m A C 88 40 kN 4m- B Prob. F3-1
The Pratt roof trusses are uniformly spaced every 15 ft. The deck, roofing material, and the purlins have an average weight of 5.6 lb/ft2. The building is located in New York where the anticipated snow load is 20 lb/ft2 and the anticipated ice load is 8 lb/ft2. These loadings occur over the
Determine the force in each member of the truss and state whether it is in tension or compression. D 2m A C -2 m O O 20 B 6 kN Prob. F3-2
Determine the force in each member of the truss and state whether it is in tension or compression. A D 3 m 0.0 B 10 kN 3 m
Determine the force in each member of the truss and state whether it is in tension or compression. 2k A D 6 ft B 8 ft Prob. F3-4
Determine the force in each member of the truss and state whether it is in tension or compression. 2 m D 00 00 2 m. с 60° 8 kN Prob. F3-5
Determine the force in each member of the truss and state whether it is in tension or compression. A -2 m H B -2 m- 600 N G -2 m- 800 N F D -2 m- 600 N 2 m E Prob. F3-6
Determine the force in members HG, HC, and BC and state whether they are in tension or compression. 600 lb A 600 lb B 600 lb H 600 lb 4 ft 4 ft-4 ft- - Prob. F3-8 600 lb F -4 ft- T 3 ft E
Determine the force in members ED, BD, and BC and state whether they are in tension or compression. -2 m- E B 18 kN -2 m. Prob. F3-9 D 6 KN 2 m
Determine the force in members GF, CF, and CD and state whether they are in tension or compression. 400 lb 400 lb HY B 400 lb -8 ft 8 ft- G C 400 lb -8 ft- Prob. F3-10 F D -8 ft 6 ft 400 lb 6 ft E
Determine the force in members FE, FC, and BC and state whether they are in tension or compression. 2 KN 1.5 m 1.5 m G -1.5 m- -3 m B 4 kN -3 m- Prob. F3-11 -3m- C 2 kN -1.5 m- E D
Determine the force in members GF, CF, and CD and state whether they are in tension or compression. 4 ft H B 500 lb 4 ft G 500 lb 4 ft Prob. F3-12 8 D 500 lb 4 ft E 1 ft 3 ft
Determine the internal normal force, shear force, and bending moment acting at point C in the beam. 20 kN-m A -2 m- +1m+1m+ Prob. F4-1 B -2 m 10 kN

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