Explanation Given information: The state of strain at a point on an element has components ε x = − 400 × 10 − 6 , ε y = 0 , and γ x y = 150 × 10 − 6 . The element oriented at an angle of 30 ° clockwise from the original position. Calculation: Apply the strain transformation Equations as shown below. Find the normal strain component in x ′ direction as shown below. ε x ′ = ε x + ε y 2 + ε x − ε y 2 cos 2 θ + γ x y 2 sin 2 θ Here, ε x is the normal strain in x direction, ε y is the normal strain in y direction, and γ x y is the shear strain of the element. Substitute − 400 × 10 − 6 for ε x , 0 for ε y , 150 × 10 − 6 for γ x y , and − 30 ° for θ . ε x ′ = [ ( − 400 × 10 − 6 ) + 0 2 + ( − 400 × 10 − 6 ) − ( 0 ) 2 cos 2 ( − 30 ° ) + ( 150 × 10 − 6 ) 2 sin 2 ( − 30 ° ) ] = ( − 200 × 10 − 6 ) − ( 200 × 10 − 6 × 0.5 ) + ( 75 × 10 − 6 × ( − 0.866 ) ) = − 365 × 10 − 6 Hence, the normal strain component in x ′ direction is − 365 × 10 − 6 _ . Find the normal strain component in y ′ direction as shown below. ε y ′ = ε x + ε y 2 − ε x − ε y 2 cos 2 θ − γ x y 2 sin 2 θ Substitute − 400 × 10 − 6 for ε x , 0 for ε y , 150 × 10 − 6 for γ x y , and − 30 ° for θ . ε y ′ = [ ( − 400 × 10 − 6 ) + 0 2 − ( − 400 × 10 − 6 ) − ( 0 ) 2 cos 2 ( − 30 ° ) − ( 150 × 10 − 6 ) 2 sin 2 ( − 30 ° ) ] = ( − 200 × 10 − 6 ) + ( 200 × 10 − 6 × 0

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 14.8, Problem 95P

To determine

Find the equivalent in-plane strains on an element.

Sketch the deformed element due to the equivalent in-plane strains.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.8, Problem 94P

Chapter 14.8, Problem 96P

Students have asked these similar questions

what is an low pressure Heater, what are formulas, and their importance, define the diagram, and give me a script on how to explain the design of an air preheater, and how did values end up in that number. based on standards

what is an air preheater, what are formulas, and their importance, define the diagram, and give me a script on how to explain the design of an air preheater, and how did values end up in that number. based on standards

Qf, Qa,Qm, Qcon,Qfg, Qbd, Qref,Qloss ( meaning, formula, percentage, and importance of higher value na qf, qa etc)

Chapter 14 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 14.3 - In each ease, the state of stress x, y, xy...Ch. 14.3 - Given the state of stress shown on the element,...Ch. 14.3 - Determine the normal stress and shear stress...Ch. 14.3 - Prob. 2FP Ch. 14.3 - Determine the equivalent state of stress on an...Ch. 14.3 - Prob. 4FP Ch. 14.3 - The beam is subjected to the load at its end....Ch. 14.3 - Prob. 6FP Ch. 14.3 - Prove that the sum of the normal stresses x+y=x+y...Ch. 14.3 - Determine the stress components acting on the...

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.

Find the equivalent in-plane strains on an element. Sketch the deformed element due to the equivalent in-plane strains.

Solution Summary: The author illustrates how to find the equivalent in-plane strains on an element.

Videos

Find the equivalent in-plane strains on an element. Sketch the deformed element due to the equivalent in-plane strains.

Want to see the full answer?

Chapter 14 Solutions

Find the equivalent in-plane strains on an element.

Sketch the deformed element due to the equivalent in-plane strains.