PROBLEMS For the following problems, unless noted otherwise, refer to Appendices F and/or G for necessary...

  
 
 

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PROBLEMS For the following problems, unless noted otherwise, refer to Appendices F and/or G for necessary mechanical prop- erties. Section 4-1 Poisson's Ratio A 1. A 2 in. diameter AISI 1020 steel rod is 10 ft long. Under an applied load, the rod elongates by 0.48 in. (a) Compute the axial (longitudinal) strain in the bar. (b) If the transverse deformation of the rod is 0.0024 in., compute Poisson's ratio for the material. 11 D 2. A rectangular ASTM A36 steel bar 2 in. by 6 in. in cross section is subjected to an axial tensile load of 300,000 lb. The proportional limit of the steel is 34,000 psi. Compute the change in the transverse 6 in. dimen- sion. 3. Modulus of elasticity, modulus of rigidity, and Pois- son's ratio are interrelated. (a) Calculate G for E = 30,000,000 psi and μ = 0.28. (b) Calculate for E = 16,000,000 psi and G = 6,000,000 psi. н н Section 4-3 Members Composed of Two or More Materials 8. A 4 in. by 8 in. short wood post is reinforced on all four sides by ASTM A36 steel plates. Two plates are 4 in. by in. thick and two plates are 8 in. by in. thick. Using nominal dimensions, calculate the maximum ax- ial compressive load that the member can safely carry. The wood is southern pine. The allowable stress is 20,000 psi for the steel. 9. The cables of a power line are copper-coated steel wire. The overall diameter of the wire is in. The steel core has a diameter of in. If the maximum tension in a wire is 10,000 lb, what are the stresses in the steel and the copper? 10. A 5 in. by 11 in. Douglas fir column and a Hem-fir column of the same size are bolted together to form a short composite column, as shown in Fig. 4-20. What portion of a total load of 70,000 lb will each material carry? 11. For the short column in Fig. 4-21, assuming that lat- eral buckling is prevented, (a) calculate the magnitude of the axial load P that will cause the total length of the member to decrease by 0.01 in. and (b) calculate the compressive stress in the steel. 112 Chapter 4 Stress Considerations 13. A lon duced radius tensil sile s from stres mum 14. A le circ allo culi bar Sectio 15. Ar in. lb pl 70,000 b 11.5 FIGURE 4-20 Problem 10. 12" # Steel (ASTM A36) A = 4.0 in Cast iron A = 9.0 in ² st C 16. / 17. 11 FIGURE 4-21 Problem 11. Section 4-4 Stress Concentration 12. A 1.0 in. diameter hole is drilled on the centerline of a long, flat steel bar which is in. thick and 4 in. wide. The bar is subjected to a tensile load of 30,000 lb. Calculate the average stress in the plane of the reduced cross section and the maximum tensile stress immedi- ately adjacent to the hole. Stress Considerations 13. A long, flat steel bar 4 in. wide and I in. thick is re- duced in width to 3 in. There are circular fillets of in. radius on each side. If the bar is subjected to an axial tensile load of 12,000 lb, calculate (a) the average ten- sile stress in the wide portion of the bar some distance from the change in section, (b) the average tensile stress in the narrow part of the bar, and (c) the maxi- mum tensile stress adjacent to the circular fillet. 14. A long, flat steel bar 5 in. wide and in. thick has a circular hole 2 in. in diameter, centrally located. The allowable tensile stress for the steel is 22,000 psi. Cal- culate the axial tensile load that may be applied to the bar. Section 4-5 Stresses on Inclined Planes 15. An aluminum specimen of circular cross section, 0.500 in. in diameter, ruptured under a tensile load of 12,000 Ib. The plane of failure was found to be at 48° with a plane perpendicular to the longitudinal axis of the specimen. (a) Compute the shear stress on the failure plane. (b) Compute the maximum tensile stress. (c) Compute the tensile stress on the failure plane. 16. A prismatic bar, 2 in. by 3 in. in cross section, is sub- jected to an axial tensile load of 110,000 lb. (a) Com- pute the maximum shear stress developed in the bar. (b) Compute the shear stress and tensile stress on a plane whose normal is inclined at 70° to the line of action of the axial load. 17. A short, square steel bar, I in. by 1 in. in cross section. is subjected to an axial tensile load of 8000 lb. Compute the shear stress and tensile stress acting on a plane whose normal is inclined at 60° to the longitudinal axis of the member. Section 4-7 Tension and Compression Caused by Shear 18. An element in a member is subjected to a pure shear of 10,000 psi. (a) Sketch the element and show the shear forces. (b) Determine the tensile normal stress on 3 plane at 35° with the horizontal. Show this plane on the sketch. on 19. For the element of Problem 18, (a) locate the plane which the shear stress is 6000 psi and (b) verify your answer by showing that a summation of forces parallel to the plane does equal zero. erline of a in, wide.. 30,000 lb. ne reduced Sectis PROBLEMS For the following problems, unless noted otherwise, refer to Appendices F and/or G for necessary mechanical prop- erties. Section 4-1 Poisson's Ratio A 1. A 2 in. diameter AISI 1020 steel rod is 10 ft long. Under an applied load, the rod elongates by 0.48 in. (a) Compute the axial (longitudinal) strain in the bar. (b) If the transverse deformation of the rod is 0.0024 in., compute Poisson's ratio for the material. 11 D 2. A rectangular ASTM A36 steel bar 2 in. by 6 in. in cross section is subjected to an axial tensile load of 300,000 lb. The proportional limit of the steel is 34,000 psi. Compute the change in the transverse 6 in. dimen- sion. 3. Modulus of elasticity, modulus of rigidity, and Pois- son's ratio are interrelated. (a) Calculate G for E = 30,000,000 psi and μ = 0.28. (b) Calculate for E = 16,000,000 psi and G = 6,000,000 psi. н н Section 4-3 Members Composed of Two or More Materials 8. A 4 in. by 8 in. short wood post is reinforced on all four sides by ASTM A36 steel plates. Two plates are 4 in. by in. thick and two plates are 8 in. by in. thick. Using nominal dimensions, calculate the maximum ax- ial compressive load that the member can safely carry. The wood is southern pine. The allowable stress is 20,000 psi for the steel. 9. The cables of a power line are copper-coated steel wire. The overall diameter of the wire is in. The steel core has a diameter of in. If the maximum tension in a wire is 10,000 lb, what are the stresses in the steel and the copper? 10. A 5 in. by 11 in. Douglas fir column and a Hem-fir column of the same size are bolted together to form a short composite column, as shown in Fig. 4-20. What portion of a total load of 70,000 lb will each material carry? 11. For the short column in Fig. 4-21, assuming that lat- eral buckling is prevented, (a) calculate the magnitude of the axial load P that will cause the total length of the member to decrease by 0.01 in. and (b) calculate the compressive stress in the steel. 112 Chapter 4 Stress Considerations 13. A lon duced radius tensil sile s from stres mum 14. A le circ allo culi bar Sectio 15. Ar in. lb pl 70,000 b 11.5 FIGURE 4-20 Problem 10. 12" # Steel (ASTM A36) A = 4.0 in Cast iron A = 9.0 in ² st C 16. / 17. 11 FIGURE 4-21 Problem 11. Section 4-4 Stress Concentration 12. A 1.0 in. diameter hole is drilled on the centerline of a long, flat steel bar which is in. thick and 4 in. wide. The bar is subjected to a tensile load of 30,000 lb. Calculate the average stress in the plane of the reduced cross section and the maximum tensile stress immedi- ately adjacent to the hole. Stress Considerations 13. A long, flat steel bar 4 in. wide and I in. thick is re- duced in width to 3 in. There are circular fillets of in. radius on each side. If the bar is subjected to an axial tensile load of 12,000 lb, calculate (a) the average ten- sile stress in the wide portion of the bar some distance from the change in section, (b) the average tensile stress in the narrow part of the bar, and (c) the maxi- mum tensile stress adjacent to the circular fillet. 14. A long, flat steel bar 5 in. wide and in. thick has a circular hole 2 in. in diameter, centrally located. The allowable tensile stress for the steel is 22,000 psi. Cal- culate the axial tensile load that may be applied to the bar. Section 4-5 Stresses on Inclined Planes 15. An aluminum specimen of circular cross section, 0.500 in. in diameter, ruptured under a tensile load of 12,000 Ib. The plane of failure was found to be at 48° with a plane perpendicular to the longitudinal axis of the specimen. (a) Compute the shear stress on the failure plane. (b) Compute the maximum tensile stress. (c) Compute the tensile stress on the failure plane. 16. A prismatic bar, 2 in. by 3 in. in cross section, is sub- jected to an axial tensile load of 110,000 lb. (a) Com- pute the maximum shear stress developed in the bar. (b) Compute the shear stress and tensile stress on a plane whose normal is inclined at 70° to the line of action of the axial load. 17. A short, square steel bar, I in. by 1 in. in cross section. is subjected to an axial tensile load of 8000 lb. Compute the shear stress and tensile stress acting on a plane whose normal is inclined at 60° to the longitudinal axis of the member. Section 4-7 Tension and Compression Caused by Shear 18. An element in a member is subjected to a pure shear of 10,000 psi. (a) Sketch the element and show the shear forces. (b) Determine the tensile normal stress on 3 plane at 35° with the horizontal. Show this plane on the sketch. on 19. For the element of Problem 18, (a) locate the plane which the shear stress is 6000 psi and (b) verify your answer by showing that a summation of forces parallel to the plane does equal zero. erline of a in, wide.. 30,000 lb. ne reduced Sectis

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