menu
bartleby
search
close search
Hit Return to see all results
close solutoin list

A cube of cast iron with sides of length a = 4.0 in. (see figure) is tested in a laboratory under triaxialsire.ss. Gages mounted on the testing machine show that the compressive strains in the material arc a = -225 X l06and,a y = 37.5 X l0_. Determine the following quantities: (a) the norm al stresses i. r,.. and acting on the x, y, and z faces of the cube; (b) the maximum shear stress r in the material; (C) the change ..W in the volume of the cube: (d) the strain energy U stored in the cube; (e) the maximum value of s when the change in volume must be limited to O.O28%; and (f) the required value of when the strain energy must be 38 in.-lb. (Assume £ = 14,000 ksi and v = 0.25.)

BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

Solutions

Chapter
Section
BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.6.5P
Textbook Problem
43 views

A cube of cast iron with sides of length a = 4.0 in. (see figure) is tested in a laboratory under triaxialsire.ss. Gages mounted on the testing machine show that the compressive strains in the material arc a

= -225 X l06and,ay = 37.5 X l0_.

Determine the following quantities: (a) the norm al stresses i. r,.. and acting on the x, y, and z faces of the cube; (b) the maximum shear stress r in the material; (C) the change ..W in the volume of the cube: (d) the strain energy U stored in the cube; (e) the maximum value of s when the change in volume must be limited to O.O28%; and (f) the required value of when the strain energy must be 38 in.-lb. (Assume £ = 14,000 ksi and v = 0.25.)

  Chapter 7, Problem 7.6.5P, A cube of cast iron with sides of length a = 4.0 in. (see figure) is tested in a laboratory under

(a)

To determine

The normal stresses acting on the x , y and z faces of the cube.

Explanation of Solution

Given information:

A cube of cast iron having side 4 in is tested under triaxial stress. The strain in the x direction is 225 × 10 6 , strain in y direction and z direction is equal which is 37.5 × 10 6 . The modulus of elasticity is 14000 ksi and the Poisson’s ratio is 0.25 .

Explanation:

Write the expression for the stress along x axis.

   σ x = E ( 1 + ν ) ( 1 2 ν ) [ ( 1 ν ) ε x + ν ( ε y + ε z ) ] ...... (I)

Here, the stress along x axis is σ x , modulus of elasticity is E , the Poisson’s ratio is ν , strain along x axis is ε x , strain along y axis is ε y and strain along z axis is ε z .

Write the expression for stress along y axis.

   σ y = E ( 1 + ν ) ( 1 2 ν ) [ ( 1 ν ) ε y + ν ( ε x + ε z ) ] ...... (II)

Here, stress along y axis is σ y .

Write the expression for stress along z axis.

   σ z = E ( 1 + ν ) ( 1 2 ν ) [ ( 1 ν ) ε z + ν ( ε x + ε y ) ] ...... (III)

Here, stress along z axis is σ z .

Calculation:

Substitute 225 × 10 6 for ε x , 37.5 × 10 6 for ε y , 37.5 × 10 6 for ε z , 14000 ksi for E and 0.25 for ν in Equation (I).

   σ x = 14000 ksi ( 1 + 0.25 ) ( 1 ( 2 × 0.25 ) ) [ ( 1 0.25 ) ( 225 × 10 6 ) + 0.25 ( 37.5 × 10 6 37.5 × 10 6 ) ] = 14000 ksi × ( 187.5 × 10 6 ) 0.625 = 4.2 ksi × ( 10 3 psi 1 ksi ) = 4200 psi

Substitute 225 × 10 6 for ε x , 37

(b)

To determine

The maximum shear stress in the material.

(c)

To determine

The change in the volume of the cube.

(d)

To determine

The strain energy stored in the cube.

(e)

To determine

The maximum value of normal stress along the x axis.

(f)

To determine

The required value of strain along the x axis.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 7 Solutions

Mechanics of Materials (MindTap Course List)
Show all chapter solutions
add
Ch. 7 - The polyethylene liner of a settling pond is...Ch. 7 - Solve the preceding problem if the norm al and...Ch. 7 - Two steel rods are welded together (see figure):...Ch. 7 - Repeat the previous problem using ? = 50° and...Ch. 7 - A rectangular plate of dimensions 3.0 in. × 5.0...Ch. 7 - Solve the preceding problem for a plate of...Ch. 7 - A simply supported beam is subjected to point load...Ch. 7 - Repeat the previous problem using sx= 12 MPa.Ch. 7 - At a point on the surface of an elliptical...Ch. 7 - Solve the preceding problem for sx= 11 MPa and...Ch. 7 - An clement m plane stress from the frame of a...Ch. 7 - Solve the preceding problem for the element shown...Ch. 7 - : A gusset plate on a truss bridge is in plane...Ch. 7 - The surface of an airplane wing is subjected to...Ch. 7 - At a point on the web of a girder on an overhead...Ch. 7 - -26 A rectangular plate of dimensions 125 mm × 75...Ch. 7 - -27 A square plate with side dimension of 2 in. is...Ch. 7 - The stresses acting on an element are x= 750 psi,...Ch. 7 - Repeat the preceding problem using sx= 5.5 MPa....Ch. 7 - An element in plane stress is subjected to...Ch. 7 - -4. - An element in plane stress is subjected to...Ch. 7 - An element in plane stress is subjected to...Ch. 7 - The stresses acting on element A in the web of a...Ch. 7 - The normal and shear stresses acting on element A...Ch. 7 - An element in plane stress from the fuselage of an...Ch. 7 - -9The stresses acting on element B in the web of a...Ch. 7 - The normal and shear stresses acting on element B...Ch. 7 - ‘7.3-11 The stresses on an element are sx= -300...Ch. 7 - - 7.3-12 A simply supported beam is subjected to...Ch. 7 - A shear wall in a reinforced concrete building is...Ch. 7 - The state of stress on an element along the...Ch. 7 - -15 Repeat the preceding problem using ??. = - 750...Ch. 7 - A propeller shaft subjected to combined torsion...Ch. 7 - 3-17 The stresses at a point along a beam...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - At a point on the web of a girder on a gantry...Ch. 7 - The stresses acting on a stress element on the arm...Ch. 7 - The stresses at a point on the down tube of a...Ch. 7 - An element in plane stress on the surface of an...Ch. 7 - A simply supported wood beam is subjected to point...Ch. 7 - A simply supported wood beam is subjected to point...Ch. 7 -   Ch. 7 - .4-2 An element in uniaxial stress is subjected to...Ch. 7 - An element on the gusset plate in Problem 7.2-23...Ch. 7 - An element on the top surface of the fuel tanker...Ch. 7 - An element on the top surface of the fuel tanker...Ch. 7 - An element in biaxial stress is subjected to...Ch. 7 - • - 7.4-7 An element on the surface of a drive...Ch. 7 - - A specimen used in a coupon test has norm al...Ch. 7 - A specimen used in a coupon test is shown in the...Ch. 7 - The rotor shaft of a helicopter (see figure part...Ch. 7 - An element in pure shear is subjected to stresses...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - Through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - 1 A rectangular steel plate with thickness t = 5/8...Ch. 7 - Solve the preceding problem if the thickness of...Ch. 7 - The state of stress on an element of material is...Ch. 7 - An element of a material is subjected to plane...Ch. 7 - Assume that the normal strains x and y , for an...Ch. 7 - A cast-iron plate in biaxial stress is subjected...Ch. 7 - Solve the preceding problem for a steel plate with...Ch. 7 - • - 3 A rectangular plate in biaxial stress (see...Ch. 7 - Solve the preceding problem for an aluminum plate...Ch. 7 - A brass cube of 48 mm on each edge is comp ressed...Ch. 7 - 7.5-11 in. cube of concrete (E = 4.5 X 106 psi. v...Ch. 7 - -12 A square plate of a width h and thickness t is...Ch. 7 - Solve the preceding problem for an aluminum plate...Ch. 7 - A circle of a diameter d = 200 mm is etched on a...Ch. 7 - The normal stress on an elastomeric rubber pad in...Ch. 7 - A rubber sheet in biaxial stress is subjected to...Ch. 7 - An element of aluminum is subjected to tri-axial...Ch. 7 - An element of aluminum is subjected to tri- axial...Ch. 7 - -3 An element of aluminum in the form of a...Ch. 7 - Solve the preceding problem if the element is...Ch. 7 - A cube of cast iron with sides of length a = 4.0...Ch. 7 - Solve the preceding problem if the cube is granite...Ch. 7 - An element of aluminum is subjected to iriaxial...Ch. 7 - Solve the preceding problem if the material is...Ch. 7 - A rubber cylinder R of length L and cross-...Ch. 7 - A block R of rubber is confined between plane...Ch. 7 - -11 A rubber cube R of a side L = 3 in. and cross-...Ch. 7 - A copper bar with a square cross section is...Ch. 7 - A solid spherical ball of magnesium alloy (E = 6.5...Ch. 7 - A solid steel sphere (E = 210 GPa, v = 0.3) is...Ch. 7 - A solid bronze sphere (volume modulus of...Ch. 7 - An element of material in plain strain has the...Ch. 7 - An clement of material in plain strain has the...Ch. 7 - An element of material in plain strain is...Ch. 7 - An element of material in plain strain is...Ch. 7 - A thin rectangular plate in biaxial stress is...Ch. 7 - Solve the preceding problem if b = 180 mm and b =...Ch. 7 - A thin square plate in biaxial stress is subjected...Ch. 7 - Solve the preceding problem if b = 225 mm. x = 845...Ch. 7 - An clement of material subjected to plane strain...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - The strains for an element of material in plane...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - An clement of material in plane strain (see...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - A brass plate with a modulus of elastici ty E = 16...Ch. 7 - Solve the preceding problem if the plate is made...Ch. 7 - An element in plane stress is subjected to...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - During a test of an airplane wing, the strain gage...Ch. 7 - A strain rosette (see figure) mounted on the...Ch. 7 - A solid circular bar with a diameter of d = 1.25...Ch. 7 - A cantilever beam with a rectangular cross section...Ch. 7 - Solve the preceding problem if the cross-...Ch. 7 - A 600 strain rosette, or delta rosette, consists...Ch. 7 - On the surface of a structural component in a...Ch. 7 - - 7.2-26 The strains on the surface of an...Ch. 7 - Solve Problem 7.7-9 by using Mohr’s circle for...Ch. 7 - 7.7-28 Solve Problem 7.7-10 by using Mohr’s circle...Ch. 7 - Solve Problem 7.7-11 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-12 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-13 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-14 by using Mohr’s circle for...

Additional Engineering Textbook Solutions

Find more solutions based on key concepts
Show solutions add
What would happen to the output of an AC generator if one of the stator windings has an open?

Automotive Technology: A Systems Approach (MindTap Course List)

Define each of the following terms: a. data b. field c. record d. file

Database Systems: Design, Implementation, & Management

Why is important to know integral calculus?

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

What is a mandatory access control?

Management Of Information Security

Compute the moment amplification factorB1 for the member of Problem 6.2-2. a. Use LRFD. b. Use ASD.

Steel Design (Activate Learning with these NEW titles from Engineering!)

Phishing Scam You just received an email message from someone requesting personal identification information. B...

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)

Which plate heats up faster on a tee joint? Why?

Welding: Principles and Applications (MindTap Course List)

If your motherboard supports ECC DDR3 memory, can you substitute non-ECC DDR3 memory?

A+ Guide to Hardware (Standalone Book) (MindTap Course List)