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engineering
structural analysis
Questions and Answers of
Structural Analysis
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
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
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
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
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
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.
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
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
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.
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.
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.
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
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.
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.
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
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
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
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
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
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.
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
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
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.
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 =
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
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
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
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
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
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
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
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.
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
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
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
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
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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