Explanation Given: Original diameter of steel ball is 40 mm . Hydrostatic pressure is 2 GPa . Concept used: Write the expression for total strain in sphere as per Hooke’s law. ε 1 + ε 2 + ε 3 = 1 − 2 v E ( σ 1 + σ 2 + σ 3 ) …… (1) Here, ε 1 , ε 2 and ε 3 are the strains in three direction for sphere , σ 1 , σ 2 and σ 3 are the stresses in all three directions, E is the modulus of elasticity of material and v is the Poisson ratio for material. For sphere which is subjected to hydrostatic pressure the magnitude of all three stresses will be same and magnitude of all three strains will be same. Substitute ε for ε 1 , ε for ε 2 , ε for ε 3 , − p for σ 1 , − p for σ 2 and − p for σ 3 in equation (1). ε + ε + ε = 1 − 2 v E ( − p − p − p ) 3 ε = 1 − 2 v E ( − 3 p ) Simplify above expression

6th Edition

ISBN: 9780134425115

Author: Schmid

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 2, Problem 2.79P

To determine

Final diameter of solid steel ball.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 2.78P

Chapter 2, Problem 2.80P

Students have asked these similar questions

The piston rod of an air operated press is to exert a maximum force of 20 kN. During the application of the force, the air pressure is maintained at 700 kPa. Assume the piston rod length to be 760mm, with its right hand end pin connected to the operating lever and the piston end of the rod fix ended. If the piston rod diameter is 15mm, determine its slenderness ratio

A thin-walled hollow sphere 3.8 m in diameter holds helium gas at 1767 kPa. Determine the minimum wall thickness of the sphere in mm if its allowable stress is 84.8 MPa.

A cube of steel with sides 2 cm long is placed in a pressure chamber. The pressure is increased until it reaches 15 atmospheres (15 x 101 kPa). What is the hydrostatic stress in the steel cube?

Chapter 2 Solutions

EBK MANUFACTURING PROCESSES FOR ENGINEE

Ch. 2 - Prob. 2.1Q Ch. 2 - Prob. 2.2Q Ch. 2 - Prob. 2.3Q Ch. 2 - Prob. 2.4Q Ch. 2 - Prob. 2.5Q Ch. 2 - Prob. 2.6Q Ch. 2 - Prob. 2.7Q Ch. 2 - Prob. 2.8Q Ch. 2 - Prob. 2.9Q Ch. 2 - Prob. 2.10Q

Ch. 2 - Prob. 2.11Q Ch. 2 - Prob. 2.12Q Ch. 2 - Prob. 2.13Q Ch. 2 - Prob. 2.14Q Ch. 2 - Prob. 2.15Q Ch. 2 - Prob. 2.16Q Ch. 2 - Prob. 2.17Q Ch. 2 - Prob. 2.18Q Ch. 2 - Prob. 2.19Q Ch. 2 - Prob. 2.20Q Ch. 2 - Prob. 2.21Q Ch. 2 - Prob. 2.22Q Ch. 2 - Prob. 2.23Q Ch. 2 - Prob. 2.24Q Ch. 2 - Prob. 2.25Q Ch. 2 - Prob. 2.26Q Ch. 2 - Prob. 2.27Q Ch. 2 - Prob. 2.28Q Ch. 2 - Prob. 2.29Q Ch. 2 - Prob. 2.30Q Ch. 2 - Prob. 2.31Q Ch. 2 - Prob. 2.32Q Ch. 2 - Prob. 2.33Q Ch. 2 - Prob. 2.34Q Ch. 2 - Prob. 2.35Q Ch. 2 - Prob. 2.36Q Ch. 2 - Prob. 2.37Q Ch. 2 - Prob. 2.38Q Ch. 2 - Prob. 2.39Q Ch. 2 - Prob. 2.40Q Ch. 2 - Prob. 2.41Q Ch. 2 - Prob. 2.42Q Ch. 2 - Prob. 2.43Q Ch. 2 - Prob. 2.44Q Ch. 2 - Prob. 2.45Q Ch. 2 - Prob. 2.46Q Ch. 2 - Prob. 2.47Q Ch. 2 - Prob. 2.48Q Ch. 2 - Prob. 2.49P Ch. 2 - Prob. 2.50P Ch. 2 - Prob. 2.51P Ch. 2 - Prob. 2.52P Ch. 2 - Prob. 2.53P Ch. 2 - Prob. 2.54P Ch. 2 - Prob. 2.55P Ch. 2 - Prob. 2.56P Ch. 2 - Prob. 2.57P Ch. 2 - Prob. 2.58P Ch. 2 - Prob. 2.59P Ch. 2 - Prob. 2.60P Ch. 2 - Prob. 2.61P Ch. 2 - Prob. 2.62P Ch. 2 - Prob. 2.63P Ch. 2 - Prob. 2.64P Ch. 2 - Prob. 2.65P Ch. 2 - Prob. 2.66P Ch. 2 - Prob. 2.67P Ch. 2 - Prob. 2.68P Ch. 2 - Prob. 2.69P Ch. 2 - Prob. 2.70P Ch. 2 - Prob. 2.71P Ch. 2 - Prob. 2.72P Ch. 2 - Prob. 2.73P Ch. 2 - Prob. 2.74P Ch. 2 - Prob. 2.75P Ch. 2 - Prob. 2.76P Ch. 2 - Prob. 2.78P Ch. 2 - Prob. 2.79P Ch. 2 - Prob. 2.80P Ch. 2 - Prob. 2.81P Ch. 2 - Prob. 2.82P Ch. 2 - Prob. 2.83P Ch. 2 - Prob. 2.84P Ch. 2 - Prob. 2.85P Ch. 2 - Prob. 2.86P Ch. 2 - Prob. 2.87P Ch. 2 - Prob. 2.88P Ch. 2 - Prob. 2.89P Ch. 2 - Prob. 2.90P Ch. 2 - Prob. 2.91P Ch. 2 - Prob. 2.92P Ch. 2 - Prob. 2.93P Ch. 2 - Prob. 2.94P Ch. 2 - Prob. 2.95P Ch. 2 - Prob. 2.96P Ch. 2 - Prob. 2.97P Ch. 2 - Prob. 2.98P Ch. 2 - Prob. 2.99P Ch. 2 - Prob. 2.100P Ch. 2 - Prob. 2.101P

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.

Final diameter of solid steel ball.

Solution Summary: The author explains how to write the expression for total strain in sphere as per Hooke's law.

Videos

Final diameter of solid steel ball.

Want to see the full answer?

Chapter 2 Solutions