Please answer with full steps and drawings please 1. A thin rectangular plate a = 20 mm x b = 12 mm (see figure below) is acted upon by a stressdistribution resulting in the uniform strains ɛ, = 300 µ, ɛ, = 500 µ, and y.y = 200 µ. Determine thefollowing:(a) The change in length of diagonal AC(b) The shear strain, yxy, along the length of diagonal AC(c) The maximum shear strain, VMax, in the plate

1. A thin rectangular plate a = 20 mm x b = 12 mm (see figure below) is acted upon by a stress distribution resulting in the uniform strains e, = 300 µ, E, = 500 µ, and y.y = 200 µ. Determine the following: (a) The change in length of diagonal AC (b) The shear strain, yxr, along the length of diagonal AC (c) The maximum shear strain, YMax, in the plate - a -

1. A thin rectangular plate a = 20 mm x b = 12 mm (see figure below) is acted upon by a stress distribution resulting in the uniform strains e, = 300 µ, E, = 500 µ, and y.y = 200 µ. Determine the following: (a) The change in length of diagonal AC (b) The shear strain, yxr, along the length of diagonal AC (c) The maximum shear strain, YMax, in the plate - a -

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.5.8P: • - 3 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses u = 67 MPa...

See similar textbooks

Similar questions

• - 3 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses u = 67 MPa (tension) and s = -23 MPa (compression). The plate has dimensions 400 X 550 X 20 mm and is made of steel with E = 200 GPa and v = 0.30. (a) Determine the maximum in-plane shear strain ?max in the plate. (b) Determine the change ?t in the thickness of the plate. (c) Determine the change ?t in the volume of the plate.
A circular aluminum tube of length L = 600 mm is loaded in compression by forces P (see figure). The outside and inside diameters are d2= 75 mm and d1= 63 mm, respectively. A strain gage is placed on the outside of the lube to measure normal strains in the longitudinal direction. Assume that E = 73 GPa and Poissons ratio is v = 0.33. (a) IF the compressive stress in the tube is 57 MPa, what is the load P? (b) If the measured strain is e = 78 J X 10-6, what is the shortening
7.5-11 in. cube of concrete (E = 4.5 X 106 psi. v = 0.2) is compressed in biaxial stress by means of a framework that is loaded as shown in the figure. Assuming that each load F equals 25 kips. determine the change iv in the volume of the cube and the strain energy U stored in the cube.
An element of aluminum is subjected to iriaxial stress (see figure). (a) Find the bulk modulus A^for the aluminum if the following stress and strain data are known: normal stresses are v = 5200 psi (tension), a = —4750 psi (compression); and (7_ = —3090 psi (compression) and normal strains in the v and v directions areet = 713,8 X 10_ (elongation) and £y=-502.3 x 10~6 (shortening), (b) If the element is replaced by one of magnesium, find the modulus of elasticity E and Poisson's ratio eif the following data is given: bulk modulus A' = 6,8 x 10 psi; normal stresses are trx= 4550 psi (tension), o", = —1700 psi (compression), and ex= 900 X 10"6 (elongation),
A copper wire having a diameter ofd = 4 mm is bent into a circle and held with the ends just touching (see figure), If the maximum permissible strain in the copper is = 0.0024, what is the shortest length L of wire that can be used? If L = 5.5 m, what is the maximum acceptable diameter of the wire if the maximum normal strain must remain below yield? Assume E = 120 GPa and(7K= 300 MPa.
-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
-7 The truss A BC Shawn in the figure supports a horizontal load P1= 300 lb and a vertical load P2= 9001b. Both bars have a cross-sectional area A = 2.4 in2 and are made of steel with E = 30 X 106 psi. (a) Determine the strain energy U1of the truss when the load P1acts alone (P2= 0). (b) Determine the strain energy U2when the load P2acts alone (P1= 0). (c) Determine the strain energy U3when both loads act simultaneously.
-7 A steel tube (G = 11.5 x 106 psi) has an outer diameter d2= 2.0 in. and an inner diameter dt=1,5 in. When twisted by a torque 7", the tube develops a maximum normal strain of 170 x 10-6. What is the magnitude of the applied torque T?
Plastic bar of diameter d = 32 mm is compressed in a testing device by a Force P = 190 N that is applied as shown in the figure. (a) Determine the normal and shear stresses acting: on all faces of stress elements oriented at (1 ) an angle 8 = 00, (2) an angle ?? = 22.5s, and (3) an angle ?? = 45°. In each case, show the stresses on a sketch of a properly oriented element. What are smaxtmax (b) Find smax and tmax in the plastic bar if a re-cantering spring of stiffness k is inserted into the testing device, as shown in the figure. The spring stillness is 1/6 of the axial stiffness of the plastic bar.
A slightly tapered bar AB of rectangular cross section and length L is acted upon by a force P (see figure). The width of the bar varies uniformly From b2at end A to b1at end B. The thickness t is constant. (a) Determine the strain energy U of the bar. (b) Determine the elongation ?? of the bar by equating the strain energy to the work done by the force P.
A 4.75-in, outside diameter polyethylene pipe designed to carry chemical waste is placed in a trench and bent around a quarter-circular 90° bend (see figure). The bent section of the pipe is 52 ft long. Determine the maximum compressive strain If the normal strain cannot exceed 6.1 × 10-3 , what is the maximum diameter of the pipe? If d = 4.75 in., what is the minimum acceptable length of the bent section of the pipe?
A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0,5 in, is subjected to internal pressure p = 375 psi, In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure), (a) Determine the maximum tensile stress ctniXand the maximum in-plane shear stress Tmjv in the wall of the cylinder. (b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T\ (c) If 7 = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thickness