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A circular aluminum tube of length L = 400 mm is loaded in compression by axial forces P at the ends. The ou inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measur strains in the longitudinal direction (axial direction). (a) If the measured compressive strain is ɛ = 550×10-6 , what is the shortening ô of the bar? (b) If the compressive stress in the bar is intended to be 40 MPa, what should be the load P?

A circular aluminum tube of length L = 400 mm is loaded in compression by axial forces P at the ends. The ou inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measur strains in the longitudinal direction (axial direction). (a) If the measured compressive strain is ɛ = 550×10-6 , what is the shortening ô of the bar? (b) If the compressive stress in the bar is intended to be 40 MPa, what should be the load P?

Steel Design (Activate Learning with these NEW titles from Engineering!)
Steel Design (Activate Learning with these NEW titles from Engineering!)
6th Edition
ISBN:9781337094740
Author:Segui, William T.
Publisher:Segui, William T.
Chapter1: Introduction
Section: Chapter Questions
Problem 1.5.6P: The data in Table 1.5.3 were obtained from a tensile test of a metal specimen with a rectangular...
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10:59 0.63 a. Y l KB/S VPN tutorial 1.pdf Axlal 1oads are applied to uie compounu rou inal is composeu of an aluminum segment rigidly connected between steel and bronze segments. (a) What is the stress in each material given that P = 10 kN? (b) Find the largest safe value of P if the working stresses are 120 MPa for steel, 68 MPa for aluminum, and 110 MPa for 2. Aluminum Steel A=300 mm² Bronze A=400 mm? A=600 mm² 2P 4P 3m -5m 4m bronze. Answer: a) 0one = 50 MPa; ouminum = 33.3 MPa; oel = 100 MPa ; b) P = 12KN A circular aluminum tube of length L = 400 mm is loaded in compression by axial forces P at the ends. The ou inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measur strains in the longitudinal direction (axial direction). (a) If the measured compressive strain is ɛ = 550×10-6 , what is the shortening ô of the bar? (b) If the compressive stress in the bar is intended to be 40 MPa, what should be the load P? Answer: a) 8 = 0.22 mm; b) P = 34.6 kN A force P of 70 N is applied by a rider to the front hand brake of a Brake cable, L=460 mm Hand brake pivot, A bicycle (P is the resultant of an evenly distributed pressure). As the hand brake pivots at A, a tension T develops in the 460-mm long brake cable ( A. = 1.075 mm') which elongates by ô = 0.214 mm . 3. 4. 37.5mm P (resultant Find normal stress o and strain ɛ in the brake cable. distributed 50mm pressure) -100mm Uniform brake pre Answer: o = 103.2 MPa ; ɛ = 4.65×10 A polyethylene bar having diameter d, = 4.0 inches is placed inside a steel tube having inner diameter d, = 4.01 inches (see figure). The polyethylene bar is then compressed by an axial force P. At what value of the force P will the space between the polyethylene bar and the steel tube be closed? (For polyethylene, E = 200 ksi & v = 0.4 .) 5. Steel tube d, d, Poyethylene bar Answer: P = – 15.71 kips P/2 Three wood boards, each 4 in. wide, are joined by the 3/4-in.- diameter bolt. If the working stresses for wood are 800 psi in tension and 1500 psi in bearing, find the largest allowable value of the force 6. 1 in. Р. 2 in. P/2 P. 1 in. - 3/4 in. Answer: P = 2250 lb (Bearing stress governs failure) 7. The truss ABC shown in the figure supports a horizontal load P, = 300lb and a vertical load P2 = 900 lb . Both bars have cross- sectional area E = 30×10° psi (a) Determine the strain energy U, of the truss when the load P, acts alone ( P, = 0 ). (b) Determine the strain energy U, when the load P, acts alone ( A = 2.4sq.in. and are made of steel with 30 B P,= 300 P, = 0). (c) Determine the strain energy U, when both loads act simultaneously. Why U3 + U1 + U2? |P,= 900 60 in. Answer: U, = 0.0375 in.-lb; U, = 2.57 in.- lb; U, = 2.22 in.- lb ; iources: J.M.Gere, B.J.Goodno, Mechanics of Materials, Cengage Learning; A.Pytel, J.Kiusalaas, Mechanics of Materials, Cengage Learning Motilal Nehru National Institute of Technology Allahabad, Prayagraj - 211004 Department of Applied Mechanics Session: 2021-22, AM13104 Strength of Materials – Tutorial Sheet – 01 (For B.Tech Mec., Civil and PIE) Page 2 of Shaft 200 mm diameter 8. A key of 70 mm length and 10 mm depth prevents relative rotation between the shaft and the pulley. Diameter of the shaft and pulley are 60 mm and 200 mm respectively. Let the width of the key be 'b’. If the torque T = 2200 Nm is applied to the shaft, determine the smallest safe dimension 'b' if the working shear stress for the key is 60 MPa. -70 mm key 60 mm diameter shaft Answer: b = 17.46 mm |60 kips The cast iron block with cross-sectional dimensions of 2.5 in. by 2.5 in. consists of two pieces. The pieces are prevented from sliding along the 55° inclined joint by the steel key, which is 2.5 in. long. 9. -2.5 in. Paytm Paytm Open Installed
Transcribed Image Text:10:59 0.63 a. Y l KB/S VPN tutorial 1.pdf Axlal 1oads are applied to uie compounu rou inal is composeu of an aluminum segment rigidly connected between steel and bronze segments. (a) What is the stress in each material given that P = 10 kN? (b) Find the largest safe value of P if the working stresses are 120 MPa for steel, 68 MPa for aluminum, and 110 MPa for 2. Aluminum Steel A=300 mm² Bronze A=400 mm? A=600 mm² 2P 4P 3m -5m 4m bronze. Answer: a) 0one = 50 MPa; ouminum = 33.3 MPa; oel = 100 MPa ; b) P = 12KN A circular aluminum tube of length L = 400 mm is loaded in compression by axial forces P at the ends. The ou inside diameters are 60 mm and 50 mm, respectively. A strain gage is placed on the outside of the bar to measur strains in the longitudinal direction (axial direction). (a) If the measured compressive strain is ɛ = 550×10-6 , what is the shortening ô of the bar? (b) If the compressive stress in the bar is intended to be 40 MPa, what should be the load P? Answer: a) 8 = 0.22 mm; b) P = 34.6 kN A force P of 70 N is applied by a rider to the front hand brake of a Brake cable, L=460 mm Hand brake pivot, A bicycle (P is the resultant of an evenly distributed pressure). As the hand brake pivots at A, a tension T develops in the 460-mm long brake cable ( A. = 1.075 mm') which elongates by ô = 0.214 mm . 3. 4. 37.5mm P (resultant Find normal stress o and strain ɛ in the brake cable. distributed 50mm pressure) -100mm Uniform brake pre Answer: o = 103.2 MPa ; ɛ = 4.65×10 A polyethylene bar having diameter d, = 4.0 inches is placed inside a steel tube having inner diameter d, = 4.01 inches (see figure). The polyethylene bar is then compressed by an axial force P. At what value of the force P will the space between the polyethylene bar and the steel tube be closed? (For polyethylene, E = 200 ksi & v = 0.4 .) 5. Steel tube d, d, Poyethylene bar Answer: P = – 15.71 kips P/2 Three wood boards, each 4 in. wide, are joined by the 3/4-in.- diameter bolt. If the working stresses for wood are 800 psi in tension and 1500 psi in bearing, find the largest allowable value of the force 6. 1 in. Р. 2 in. P/2 P. 1 in. - 3/4 in. Answer: P = 2250 lb (Bearing stress governs failure) 7. The truss ABC shown in the figure supports a horizontal load P, = 300lb and a vertical load P2 = 900 lb . Both bars have cross- sectional area E = 30×10° psi (a) Determine the strain energy U, of the truss when the load P, acts alone ( P, = 0 ). (b) Determine the strain energy U, when the load P, acts alone ( A = 2.4sq.in. and are made of steel with 30 B P,= 300 P, = 0). (c) Determine the strain energy U, when both loads act simultaneously. Why U3 + U1 + U2? |P,= 900 60 in. Answer: U, = 0.0375 in.-lb; U, = 2.57 in.- lb; U, = 2.22 in.- lb ; iources: J.M.Gere, B.J.Goodno, Mechanics of Materials, Cengage Learning; A.Pytel, J.Kiusalaas, Mechanics of Materials, Cengage Learning Motilal Nehru National Institute of Technology Allahabad, Prayagraj - 211004 Department of Applied Mechanics Session: 2021-22, AM13104 Strength of Materials – Tutorial Sheet – 01 (For B.Tech Mec., Civil and PIE) Page 2 of Shaft 200 mm diameter 8. A key of 70 mm length and 10 mm depth prevents relative rotation between the shaft and the pulley. Diameter of the shaft and pulley are 60 mm and 200 mm respectively. Let the width of the key be 'b’. If the torque T = 2200 Nm is applied to the shaft, determine the smallest safe dimension 'b' if the working shear stress for the key is 60 MPa. -70 mm key 60 mm diameter shaft Answer: b = 17.46 mm |60 kips The cast iron block with cross-sectional dimensions of 2.5 in. by 2.5 in. consists of two pieces. The pieces are prevented from sliding along the 55° inclined joint by the steel key, which is 2.5 in. long. 9. -2.5 in. Paytm Paytm Open Installed
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