Explanation Given information: A soft material is placed within the confines of a rigid cylinder which rests on a rigid support. Poisson’s ration is ν = 0.3 . Calculation: Assuming that ε x = 0 and ε y = 0 . Apply the normal strain in x direction as shown below. ε x = 1 E ( σ x − ν ( σ y + σ z ) ) Here, E is the modulus of elasticity, σ x is the normal stress in x direction, ν is the Poisson’s ratio, σ y is the normal stress in y direction, and σ z is the normal stress in z direction. Substitute 0 for ε x . 0 = 1 E ( σ x − ν ( σ y + σ z ) ) σ x − ν ( σ y + σ z ) = 0 (1) Apply the normal strain in y direction as shown below. ε y = 1 E ( σ y − ν ( σ x + σ z ) ) Substitute 0 for ε y . 0 = 1 E ( σ y − ν ( σ x + σ z ) ) σ y − ν ( σ x + σ z ) = 0 (2) Equating Equations (1) and (2). σ x − σ y = ν ( σ y + σ z ) − ν ( ) σ x − σ y = ν ( σ y + σ z − σ x − σ z ) σ x − σ y = − ν ( σ x − σ y ) ( σ x − σ y ) + ν ( σ x − σ y ) = 0 ( 1 + ν ) ( σ x − σ y ) = 0 σ x − σ y = 0 σ x = σ y Substitute σ x for σ y in Equation (1). σ x − ν ( σ x + σ z ) = 0 ( 1 − ν ) σ x − ν σ z = 0 ( 1 − ν ) σ x = ν σ z σ x = ν ( 1 − ν ) σ z Hence, σ y = ν ( 1 − ν ) σ z . Apply the normal strain in z direction as shown below. ε z = 1 E ( σ z − ν ( σ x + σ y ) ) Substitute ν ( 1 − ν ) σ z for σ x and ν ( 1 − ν ) σ z for σ y

9th Edition

ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

See similar textbooks

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

Videos

Question

100%

Chapter 10.6, Problem 10.58P

To determine

The increase factor by which the stiffness of the material, or the apparent modulus of elasticity.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.6, Problem 10.57P

Chapter 10.7, Problem 10.59P

Students have asked these similar questions

. A 175-lb woman stands on a vinyl floor wearing stiletto high-heel shoes. If the heel has the dimensions shown, determine the average normal stress she exerts on the floor and compare it with the average normal stress developed when a man having the same weight is wearing flat-heeled shoes. Assume the load is applied slowly, so that dynamic effects can be ignored. Also, assume the entire weight is supported only by the heel of one shoe. Solution: - For Stiletto shoes =869 psi - For Flat-heeled shoes =50.5 psi

The load of 2000 lb is to be supported by the two vertical steel wires for which sY = 70 ksi. Originally wire AB is 60 in. long and wire AC is 60.04 in. long. Determine the cross-sectional area of AB if the load is to be shared equally between both wires. Wire AC has a cross-sectional area of 0.02 in2. Est = 29.0(103) ksi.

Before the load is placed on the rigid plate, the top of the central spring is 20 mm lower than the outer springs. Each outer spring is made of 24 turns of 15-mm diameter wire on a mean radius of 60 mm. The central spring consists of 16 turns of 20 mm dimeter wire on a mean radius of 80 mm. If a load P = 5 kN is now placed on the rigid plate. Disregarding the weight of the plate, use G = 83 GPa and use Light spring formula. Determine the maximum shearing stress of the in uter spring. In MPa

Chapter 10 Solutions

Mechanics Of Materials, Si Edition

Ch. 10.3 - Prove that the sum of the normal strains in...Ch. 10.3 - The state of strain at the point on the arm has...Ch. 10.3 - Prob. 10.3P Ch. 10.3 - Prob. 10.4P Ch. 10.3 - 10-5. The state of strain at the point on the gear...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Prob. 10.8P Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain- transformation equations to...

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.

The increase factor by which the stiffness of the material, or the apparent modulus of elasticity.

Solution Summary: The author explains the increase factor by which the stiffness of the material, or the apparent modulus of elasticity, is 1.35.

Concept explainers

Videos

The increase factor by which the stiffness of the material, or the apparent modulus of elasticity.

Want to see the full answer?

Chapter 10 Solutions