The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E = 94 GPal with a cross-sectional area of A, = 240 mm?. Bar (2) is an aluminum alloy [E = 71 GPa] with a cross-sectional area of A, = 660 mm?. All bars are unstressed before the load Pis applied; however, there is a 2-mm clearance in the pin connection at A. Assume L, = 2180 mm, a = 920 mm, b = 560 mm, c = 450 mm, and L, = 1620 mm. If a load of P = 53 kN is applied at B, determine (a) the normal stresses in both bars (1) and (2). (b) the downward deflection of point A on the rigid bar. (1) a b D L2 P. (2) Answers: (a) o1 = MPa 02 = MPa (b) VA = mm

The pin-connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. Bar (1) is a bronze alloy [E = 94 GPal with a cross-sectional area of A, = 240 mm?. Bar (2) is an aluminum alloy [E = 71 GPa] with a cross-sectional area of A, = 660 mm?. All bars are unstressed before the load Pis applied; however, there is a 2-mm clearance in the pin connection at A. Assume L, = 2180 mm, a = 920 mm, b = 560 mm, c = 450 mm, and L, = 1620 mm. If a load of P = 53 kN is applied at B, determine (a) the normal stresses in both bars (1) and (2). (b) the downward deflection of point A on the rigid bar. (1) a b D L2 P. (2) Answers: (a) o1 = MPa 02 = MPa (b) VA = mm

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.3.2P: A long, rectangular copper bar under a tensile load P hangs from a pin that is supported by two...

See similar textbooks

Similar questions

Wires B and C are attached to a support at the left-hand end and to a pin-supported rigid bar at the right-hand end (see figure). Each wire has cross-sectional area A =0.03 in2 and modulus of elasticity E = 30 X 106 psi. When the bar is in a vertical position, the length of each wire is L = 80 in. However, before being attached to the bar, the length of wire B was 79.98 in. and wire C was 79.95 in. Find the tensile forces TBand Tc in the wires under the action of a force P = 700 lb acting at the upper end of the bar.
*16 A prismatic bar AB of length L, cross-sectional area A, modulus of elasticity E, and weight Changs vertically under its own weight (see figure). (a) Derive a formula for the downward displacement Scof point E. located at distance It from the lower end of the bar. (b) What is the elongation SBof the entire bar? (c) What is the ratio £ of the elongation, of the upper half of the bar to the elongation of the lower half of the bar? (d) If bar A B is a riser pipe hanging from a drill rig at sea. what is the total elongation of the pipe? Let L = 1500 m, A - 0.ol57 m2, and E = 210 GPa. See Appendix 1 for weight densities of steel and sea water. (See Probs. 1.4-2 and J.7-13 for additional figures.)
A long, rectangular copper bar under a tensile load P hangs from a pin that is supported by two steel posts (see figure). The copper bar has a length of 2.0 m, a cross-sectional area of4S00 mm", and a modulus of elasticity Ec= 120 GPa. Each steel post has a height of 0.5 m, a cross-sectional area of 4500 mm2, and a modulus of elasticity E = 200 GRa. (a) Determine the downward displacement
,10-6 A prismatic bar with a diameter d0= 20 mm is being compared with a stepped bar of the same diameter(d| = 20 mm) that is enlarged in the middle region lo a diameter d2= 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm. (a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate your answer by determining the maximum permissible load for the prismatic bar and the maximum permissible load F, for the enlarged bar, assuming that the allowable stress for the material is 80 MPa. (b) What should be the diameter d0of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar?
A round bar of 10 mm diameter is made of aluminum alloy 7075-T6 (see figure). When the bar is stretched by axial forces P, its diameter decreases by 0.0 16 mm. Find the magnitude of the load P. Obtain the material properties from Appendix 1.
A rigid bar of weight W = 750 lb hangs from three equally spaced wires: two of steel and one of aluminum (see figure). The diameter of the wires is 1/8 in. Before they were loaded, all three wires had the same length. What temperature increase T in all three wires will result in the entire load being carried by the steel wires? (Assume Es= 30 × 106 psi, as= 6.5 × 10-6 /'F, and aa= 12 × 10-6F.)
A vertical bar is loaded with axial loads at points B, C, and D. as shown in the figure. The bar is made of steel with a modulus of elasticity E = 29,000 ksi., The bar has a cross-sectional area of 8.24 in2. Calculate the displacements at points B, C, and D. Ignore the weight of the bar
A compressive load P is transmitted through a rigid plate to three magnesium-alloy bars that are identical except that initially the middle bar is slightly shorter than the other bars (see figure). The dimensions and properties of the assembly are as follows: length L = 1.0 m, cross-sectional area of each bar A = 3000 mm", modulus of elasticity E = AS GPa, and the gap s = 1.0 mm. (a) Calculate the load Ptrequired to close the gap. (b) Calculate the downward displacement 5 of the rigid plate when P = 400 kN. (c) Calculate the total strain energy V of the three bars when P = 400 kN (d) Explain why the strain -energy V is not equal to PS/2. Hint: Draw a load-displacement diagram.
A circular steel rod AB? (diameter d, = 1.0 in., length L1= 3.0 Ft) has a bronze sleeve (outer diameter d2= 1-25 in., length L2= 1.0 ft) shrunk onto it so that the two parts are securely bonded (see figure). Calculate the total elongation 6 of the steel bar ¦due to a temperature rise AT = 500°F. (Material properties are as follows: For steel, Es= 30 ×106 psi and as= 6.5 × lO6/?; for bronze, Eb= 15 × 106psi and ab= 11 × l0-6/?.)
A column ABC is supported at ends A and C and compressed by an axial load P (figure a). Lateral support is provided at point B but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at A and C. The column is constructed of two channel sections (C 6 × 8.2) back to back (see figure b). The modulus of elasticity of the column is E = 29,500 ksi and the proportional limit is 50 ksi. The height of the column is L = 15 ft. Find the allowable value of load P using a factor of safety of 2.5.
The length of the end segments of the bar (see figure) is 20 in. and the length of the prismatic middle segment is 50 in. Also, the diameters at cross sections A. B, C, and D are 0.5, 1.0, 1.0, and 0.5 in., respectively, and the modulus of elasticity is 18 ,000 ksi. (a) Calculate the elongation of a copper bar of solid circular cross section with tapered ends when it is stretched by axial loads of magnitude 3.0 kips (see figure). (b) If the total elongation of the bar cannot exceed 0.025 in., what are the required diameters at B and C? Assume that diameters at A and D remain at 0.5 in.
Around brass bar of a diameter d1= 20mm has upset ends each with a diameter d2= 26 mm (see figure). The lengths of the segments of the bar are L1= 0.3 m and L2= 0.1 m. Quarter-circular fillets are used at the shoulders of the bar, and the modulus of elasticity of the brass is E = 100 GPa. If the bar lengthens by 0.12 mm under a tensile load P, what is the maximum stress ??maxin the bar?