Concept explainers
(a)
Find the change in length of the cube in the x direction.
(a)
Answer to Problem 91P
The change in length of the cube in the x direction is
Explanation of Solution
Given information:
The modulus of elasticity in x-direction
The modulus of elasticity y-direction
The modulus of elasticity in z-direction
The strain along xz axis is 0.254.
The strain along xy axis is 0.254
The strain along zy axis is 0.428.
Calculation:
Write the stress to strain Equation along x direction as follows:
Here,
Write the stress to strain Equation along y direction as follows:
Write the stress to strain Equation along z direction as follows:
Equate the stress Equation along xy axis.
Equate the stress Equation along yz axis.
Equate the stress Equation along zx axis.
Apply the constraint conditions as follows:
Substitute 0 for
Substitute 0 for
Substitute
Substitute
Solving Equation to get values,
Apply the Equation (4) and (5) in Equation 1 as follows:
Substitute 0.254 for
Calculate the cross sectional area of cube as follows:
Here, a is the sides.
Substitute
Find the normal stress along x axis as follows:
Here, P is the tensile load and A is the cross sectional area.
Substitute
Find the strain along x axis as follows:
Substitute
Determine the change in length of the cube in the x direction using the relation:
Here,
Substitute
Thus, the change in length of the cube in the x direction is
(b)
The stress values
(b)
Answer to Problem 91P
The stress value
The stress value
The stress value
Explanation of Solution
Calculation:
Find the normal stress along x axis as follows:
Here, P is the tensile load and A is the cross sectional area.
Substitute
Thus, the stress value
Find the normal stress along y,z axis as follows:
Substitute
Thus, the stress value
Thus, the stress value
Want to see more full solutions like this?
Chapter 2 Solutions
Mechanics of Materials, 7th Edition
- A spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thickness is 0,012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.arrow_forwardA 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?arrow_forwardA joint between two glass plates A and B is filled with a flexible epoxy that bonds securely to the glass. The height of the joint is/p = 0.5 in, its length is L = 30 in, and its thickness is/ = 0.5 in. Shear force of I' = 25 kips is applied to the joint. Calculate the displacement of the joint if the shear modulus of elasticity G of the epoxy is 100 ksi. Calculate the average shear strain in the epoxy.arrow_forward
- - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?arrow_forwardLet’s consider a rod having a solid circular cross-section with diameter of 6 mm and it is made of a material having a Young’s modulus E = 200 Gpa and a Poisson’s ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 5.998 mm. determine the applied force F. Select one: F = 6283 N F = 10472 N F = 4189 N F = 5236 N F = 13090 N F = 15708 Narrow_forwardTwo solid cylindrical rods (1) and (2) are joined together at flange B and loaded, as shown. The diameter of rod (1) is d1 = 1.66 in. and the diameter of rod (2) is d2 = 2.68 in. Determine the normal stresses in rods (1) and (2). Assume P = 17 kips and Q = 29 kips. Use positive for tensile stress and negative for compressive stress.arrow_forward
- A cube of side 40 mm, subjected to 3 mutually perpendicular tensile forces of 9 kN, 5 kN, 5 kN acting along X, Y, Z directions respectively. Find the stresses in each directions and the strain along x direction of the cube. Take Young's Modulus of the material as 210 GPa, Poisson's ratio as 0.3. (ENTER ONLY THE VALUES IN THE BOXES BY REFERRING THE UNITS GIVEN IN BRACKET) (i) Stress along X direction (Unit in N/mm2) = 5.625 One possible correct answer is: 5.625 (ii) Stress along Y direction (Unit in N/mm2) = 3.125 One possible correct answer is: 3.125 (iii) Stress along Z direction (Unit in N/mm2) = 3.125 One possible correct answer is: 3.125 (iv) Strain along X direction = 1.785*10^-11arrow_forwardLet's consider a rod having a solid circular cross-section with diameter of 4 mm and it is made of a material having a Young's modulus E = 200 Gpa and a Poisson's ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 3.995 mm. determine the applied force F. Select one: F = 10472 N O F = 6283N O F= 15708 N O F = 4189N O F = 5236 N O F = 13090 N Clear my choicearrow_forwardA short post constructed from a hollow circular tube of aluminum supports a compressive load of 54 kips. The inner and outer diameters of the tube are d1=3.6 in. and d2=5.0 in., respectively, and its length is 40 in. The shortening of the post due to the load is measured as 0.022 in. Determine the compressive stress and strain in the post. (Disregard the weight of the post itself, and assume that the post does not buckle under the load.) 5arrow_forward
- 3. A steel rod of 3 cm diameter and 5 m length is connected to two grips and the rod is held at a temperature of 95 °C. Determine the stress in the rod, and the force in the rod if the temperature drops to 30 °C for the following cases a. The grip ends do not yield b. The grip ends yield by 0.12 cm Assume the Young's Modulus of the rod is E = 2×105 MPa, and the CTE is a=12×106/ °Carrow_forwardIn a volume element with dimensions dx, dy, dz the negatíve y-face has a 2 MPa stress in the positivex-direction, a 3 MPa stress in the negative z-direction, and a 4 MPa stress in the negatíve y-direction. Which of the following describes the stresses per elasticity convention? Oyy = 4 MPa Oyr = -2 MPa 3 MPa A MPaarrow_forwardLet's consider a rod having a solid circular cross-section with diameter of 5 mm and it is made of a material having a Young's modulus E = 200 Gpa and a Poisson's ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 4.995 mm. determine the applied force F.arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning