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Answer :
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Deformed shape:
Bending moment diagram(BMD):
shear force diagram:
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39. Solve the following frame structure using a commercial finite element analysis program. The f...
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2...
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2) Assume a simply supported beam of length 1 m subjected to a uniformly distributed load along its length of 100 N/cm. The modulus of elasticity is 207 GPa. The beam is of rectangular cross-section with a width equal to 0.01 m and a depth equal to 0.02 m. Using only one beam element, determine the deflection and maximum stress at midspan.
Solve the two problems...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4. Finally, draw the shear force and bending moment diagrams for each element. LetE 30 x 103 ksi, A = 8 in,2 , and 1-800 in.4 for all elements. 20 kip 25 ft 25 ft- 40 ft 20...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the fo...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4 Finally, draw the shear force and bending moment diagrams for each element. Let E 30x 103 ksi, A 8 in2, and I 800 in.4 for all elements. 20 kip 25 ft 25 ft 40 ft Figure P5-4...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total le...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total length I3 m. At its midpoint, a belt passes over a pulley and delivers 50 kW power to the shaft. This power is used to drive two machines at either end of the shaft. Machine 1 consumes P1 20 kW and machine 2 uses P230 KW. The...
Q2 (a) (0) Explain what is meant by interpolation in the Finite Element Method and why...
Q2 (a) (0) Explain what is meant by interpolation in the Finite Element Method and why it is used (3 marks) What is a shape function? (3 marks) PLEASE TURN OVER 16363,16367 Page 2 of 3 0.2 (a) (Continued) (iii) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3...
A beam may have zero shear stress at a section but may not have zero deflection;...
A beam may have zero shear stress at a section but may not have zero deflection; Hence, bending is primarily caused by bending moment In Torsion loading a stress element in a circular rod is subject to shear state The principal plane and the plane on which the shear stresses are maximum, they make 90 degree angle between them. If the Torque on a steel circular shaft (G=80 GPa) is 13.3 kN-m and the allowable shear stress is 98 MPa,...
Question 2 I (a) Using a 459 strain gauge rosette placed on a mild steel structure,...
Question 2 I (a) Using a 459 strain gauge rosette placed on a mild steel structure, the following strains were established from the measurements taken:£x = 75x10", Eyy =-115x10-6 = 210 10-6 and Yxy yy (i) Determine the corresponding normal stresses Ox and and shear stress txy. For mild steel, use Young's modulus E= 205 GPa , Poisson's ratio v=0.3 and shear modulus G = 78.8 GPa. [6 marks] (ii) Using the values obtained in (i), determine the principal stresses...
Question I.5 Figure 1.5 shows a frame with loads at A and D. Select the closest...
Question I.5 Figure 1.5 shows a frame with loads at A and D. Select the closest value for the magnitude of the total reaction at B. Assume the weight of the frame is zero. 40 kN VE 96.2 kN (a) (Ь -40 kN 5 m (c) -87.5 kN 30 kN (d) 57 kN 4m ao 1 m (e) 50 kN Figure L.5 Low mass frame Question I.6 In the shear and bending moment equations for beams, which of the following...
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2) Assume a simply supported beam of length 1 m subjected to a uniformly distributed load along its length of 100 N/cm. The modulus of elasticity is 207 GPa. The beam is of rectangular cross-section with a width equal to 0.01 m and a depth equal to 0.02 m. Using only one beam element, determine the deflection and maximum stress at midspan.
Solve the two problems...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4. Finally, draw the shear force and bending moment diagrams for each element. LetE 30 x 103 ksi, A = 8 in,2 , and 1-800 in.4 for all elements. 20 kip 25 ft 25 ft- 40 ft 20...
Solve all problems using the finite element stiffness method. For the rigid frame shown in Figure P5-4, determine (1) the nodal displacements and rotation at node 4, (2) the reactions, and (3) the forces in each element. Then check equilibrium at node 4 Finally, draw the shear force and bending moment diagrams for each element. Let E 30x 103 ksi, A 8 in2, and I 800 in.4 for all elements. 20 kip 25 ft 25 ft 40 ft Figure P5-4...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total length I3 m. At its midpoint, a belt passes over a pulley and delivers 50 kW power to the shaft. This power is used to drive two machines at either end of the shaft. Machine 1 consumes P1 20 kW and machine 2 uses P230 KW. The...
Q2 (a) (0) Explain what is meant by interpolation in the Finite Element Method and why it is used (3 marks) What is a shape function? (3 marks) PLEASE TURN OVER 16363,16367 Page 2 of 3 0.2 (a) (Continued) (iii) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3...
A beam may have zero shear stress at a section but may not have zero deflection; Hence, bending is primarily caused by bending moment In Torsion loading a stress element in a circular rod is subject to shear state The principal plane and the plane on which the shear stresses are maximum, they make 90 degree angle between them. If the Torque on a steel circular shaft (G=80 GPa) is 13.3 kN-m and the allowable shear stress is 98 MPa,...
Question 2 I (a) Using a 459 strain gauge rosette placed on a mild steel structure, the following strains were established from the measurements taken:£x = 75x10", Eyy =-115x10-6 = 210 10-6 and Yxy yy (i) Determine the corresponding normal stresses Ox and and shear stress txy. For mild steel, use Young's modulus E= 205 GPa , Poisson's ratio v=0.3 and shear modulus G = 78.8 GPa. [6 marks] (ii) Using the values obtained in (i), determine the principal stresses...
Question I.5 Figure 1.5 shows a frame with loads at A and D. Select the closest value for the magnitude of the total reaction at B. Assume the weight of the frame is zero. 40 kN VE 96.2 kN (a) (Ь -40 kN 5 m (c) -87.5 kN 30 kN (d) 57 kN 4m ao 1 m (e) 50 kN Figure L.5 Low mass frame Question I.6 In the shear and bending moment equations for beams, which of the following...
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