The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a homogeneous material. The length (L) of the rod is 1.75 m and Young’s Modulus for the material (E) is 250 GPa. When the rod is placed under tension it experiences deformation and a stress (?) of 650 MPa. Calculate the following: (1) Strain energy (U) to 2 decimal places in Joules. (2) Strain energy per unit volume (U/V) in J/m3 (3) The change in length ∆L to 2 decimal places in mm. (4) The strain (?) due to deformation to 2 significant figures. (show all work)

The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a homogeneous material. The length (L) of the rod is 1.75 m and Young’s Modulus for the material (E) is 250 GPa. When the rod is placed under tension it experiences deformation and a stress (?) of 650 MPa. Calculate the following: (1) Strain energy (U) to 2 decimal places in Joules. (2) Strain energy per unit volume (U/V) in J/m3 (3) The change in length ∆L to 2 decimal places in mm. (4) The strain (?) due to deformation to 2 significant figures. (show all work)

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.6.7P: A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The...

See similar textbooks

Related questions

Q: Same problem is considered here again using three equal length elements. Suppose that the strain…

A: Given Data :- Strain energy of element 1 ( u1) = 0.09 N.m Strain energy of element 2 ( u2) = 0.17…

Q: A very thick structure is subjected to certain traction boundary conditions on its surface. The…

A: “Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: A rigid steel bar is supported by three circular rods as shown in Figure below. There is no strain…

Q: The engineering stress-engineering tensile curve for a stainless steel typ alloy is shown. Calculate…

A: The true stress and true strain curve σt=KεtnFind K and n

Q: Stress (MPa) Graph 1 - Stress/Strain plot 400 320 300 200 100 0 (a) 51.472kN (b) 205.89kN (c) 25735N…

Q: The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a…

Q: Same problem is considered here again using three equal length elements. Suppose that the strain…

Q: sion force T is attached to a horiz ber at B and C to support a sign st passes over a small…

A: The stress-strain relationship for the wire ishere, is the strainThere are different values of the…

Q: teel plate (E = 31000 ksi, G= 12000 ksi, alpha (a) = 6 * 10 ^ -6 1/F ) with dimensions a = 20 in and…

A: GivenE=31000ksiG=12000ksiα=6×10-6 /Foa=20inb=13int=7.5inσ=-50ksi∆T=100Fo

Q: The nodal coordinates and the nodal displacements for some plane stress elastic element is listed in…

Q: A thin metal alloy plate is loaded by biaxial stress (2 directions) given by 8000 psi in the x…

Q: rod ABC is applied with axial loading as shown in Figure Q4(a). Using E = 200 GPa, determine (i) the…

A: Given:E=200 GPaP=36 KNd=16 mmD=20 mmLAB=600 mmLBC=900 mm

Q: Same problem is considered here again using three equal length elements. Suppose that the strain…

A: Given Data Strain energy of element 1 ( U1) = 0.07 N.m Strain energy of element 2 ( U2) = 0.17 N.m…

Q: Same problem is considered here again using three equal length elements. Suppose that the strain…

A: Strain energy of element 1 ( u1) = 0.09 N.m Strain energy of element 2 ( u2) = 0.17 N.m Strain…

Q: A strain rosette was attached to the outer surface of stainless vessel when the vessel is in a…

A: To find-

Q: Same problem is considered here again using three equal length elements. Suppose that the Young's…

Q: The stress-strain behaviour of a material is shown in the figure. Its resilience and toughness, in…

A: Given: Stress strain behaviour of a material,

Q: An aluminum alloy [E = 70 GPa; v = 0.33; a = 23.0x10-6/°C] pipe is subjected to a tensile load P.…

A: Young's modulus of the aluminum alloy (E): 70 GPaPoisson's ratio of the aluminum alloy (v):…

Q: The stress-strain curve of cellulose acetate at 25°C is shown below. Draw the curves at 0°C and…

A: Solution: Given Data: To Find: 1. Stress-Strain curve of cellulose acetate at 00C. 2.…

Q: An aluminum alloy [E = 70 GPa; v = 0.33; a = 23.0x10-6/°C] bar is subjected to a tensile load P. The…

A: We will calculate the longitudinal and transverse strain due to both temperature change ans load P…

Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a homogeneous material. The length (L) of the rod is 1.75 m and Young’s Modulus for the material (E) is 250 GPa. When the rod is placed under tension it experiences deformation and a stress (?) of 650 MPa. Calculate the following:
(1) Strain energy (U) to 2 decimal places in Joules.
(2) Strain energy per unit volume (U/V) in J/m³
(3) The change in length ∆L to 2 decimal places in mm.
(4) The strain (?) due to deformation to 2 significant figures. (show all work)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300
- 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?
A prismatic bar in tension has a length L = 2.0 m and cross-sectional area A =249 mn2. The material of the bar has the stress-strain curve shown in the figure. Determi ne t he elongation 5 of the bar for each of the following axial loads: P = 10 kN, 20 kN, 30 kN, 40 kN. and 45 kN. From these results, plot a diagram of load P versus elongation 5 (load-displacement diagram).
A 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.
A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?
A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).
A bar with a circular cross section having two different diameters d and 2d is shown in the figure. The length of each segment of the bar is L/2T and the modulus of elasticity of the material is E. (a) Obtain a formula for the strain energy U of the bar due to the load P. (b) Calculate the strain energy if the load P = 27 kN, the length L = 600 mm, the diameter d = 40 mm, and the material is brass with E = 105 GPa.
A bungee cord that behaves linearly elastically has an unstressed length L0= 760 mm and a stiffness k = 140 N/m. The cord is attached to two pegs, distance/? = 380 mm apart, and is pulled at its midpoint by a Force P = 80 N (see figure). (a) How much strain energy U is stored in the cord? (b) What is the displacement Scof the point where the load is applied? (c) Compare the strain energy (with the quantity PSC12. Note: The elongation of the cord is not small compared lo its original length.
-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.
An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.
An elastomeric bearing pad consisting of two steel plates bonded to a chloroprene elastomer (an artificial rubber) is subjected to a shear force V during a static loading test (see figure). The pad has dimensions a = 125 mm and b = 240 mm, and the elastomer has a thickness t = 50 mm. When the Force V equals 12 kN, the top plate is found to have displaced laterally S.O mm with respect to the bottom plate. What is the shear modulus of elasticity G of the chloroprene?
The diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and ismade from a homogeneous material. The length (L) of the rod is 1.75 m andYoung’s Modulus for the material (E) is 250 GPa. When the rod is placed undertension it experiences deformation and a stress (?) of 650 MPa. Calculate thefollowing:(i) Strain energy (U) to 2 decimal places in Joules.(ii) Strain energy per unit volume (U/V) in J/m3.(iii) The change in length ∆L to 2 decimal places in mm.(iv) The strain (?) due to deformation to 2 significant figures