For the prismatic bar in simple tension shown below, the stress state at any point "M" is characterized by Sig = p, and the other stress components are null. You are asked to determine the stress vector, as well as its normal and shear components, on a generic facet of normal parallel to the xy plane. M

For the prismatic bar in simple tension shown below, the stress state at any point "M" is characterized by Sig = p, and the other stress components are null. You are asked to determine the stress vector, as well as its normal and shear components, on a generic facet of normal parallel to the xy plane. M

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 7.7.15P: A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded...

See similar textbooks

Similar questions

A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
A circular cylindrical steel tank (see figure) contains a volatile fuel under pressure, A strain gage at point A records the longitudinal strain in the tank and transmits this information to a control room. The ultimate shear stress in the wall of the tank is 98 MPa, and a factor of safety of 2,8 is required. (a) At what value of the strain should the operators take action to reduce the pressure in the tank? (Data for the steel are modulus of elasticity E = 210 GPa and Poisson's ratio v = 0.30.) (b) What is the associated strain in the radial direction
A solid circular steel cylinder S is encasedin a hollow circular aluminum tube A. The cylinderand tube are compressed between the rigid plates ofa testing machine which applies forces P. Calculatethe allowable value of the compressive force if theyield stresses of steel and aluminum are σyS = 50 ksiand σyA = 60 ksi , respectively. Assume thatAS = 12 in2, AA = 6 in2, L = 20 in., ES = 29,000 ksi,and EA =10,600 ksi
In constructing a large mobile, Jude hangs an aluminum sphere of mass 6.0kg from a vertical steel wire 0.50m long and 2.5x10^−3 cm^2 in cross-sectional area. On the bottom of the sphere, he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0kg. For each wire, compute: (a) The tensile strain and(b) The elongation
In constructing a large mobile, Jude hangs an aluminum sphere of mass 6.0kg from a vertical steel wire 0.50m long and 2.5 x10−3 cm2 in cross-sectional area. On the bottom of the sphere, he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0kg. For each wire, compute:(a) The tensile strain and(b) The elongation
Pressure inside the cylinder is 10 bars Is this a thin walled cylinder when the thickness is 10 mm. Estimate theoretically the hoop andlongitudinal stresses
Calculate the resulting stress in an aluminum wire, 4-m long and 2.6 mm in diameter, if a 12.5 -kg fixture is hung from the wire? Young's modulus for aluminum is 7.0 × 10^10 N/m^2. Express the answer in Pa and as a whole number.
A wire with a Young’s Modulus, E, of 8.5 x 106 N/m2 and an original length of 1.5 mis under tension. If the wire length extension is 2.5 mm, calculate the stress in thewire. Give your answer in N/m2to 2 decimal places.
The plate shown below initially measures 90 X 65mm . Find the changes to these dimensions when subjected to the stresses shown. The modulus of elasticity of the material is 214 E GPA and poissons ratio is 0.32. Also derive the expressions for the change in dimensions of a cube subjected to three dimensional loading.
Find stress of a aluminum cylinder of diameter 12.8mm and gauge length 50.8mm. The force applied is 47,500N.
A cylindrical steel pressure vessel 60 cm in diameter with a wall thickness of 30 mun, is subjected to an internal pressure of 6 Nmm. (a) Calculate the tangential and longitudinal stresses in the steel. (b) To what value may the internal pressure be increased if the stress in the steel is limited to 200 MN/m?
A rectangular block of material is subjected to a tensile stress of 90 N/mm2 along X axis and acompressive stress of 45 N/mm2 on a plane at right angle to it, together with shear stresses of80 N/mm2 on the same plane. Calculate the direction of principal planes, the magnitude ofprincipal stresses and the magnitude of greatest shear stresses.