Explanation Given information: The state of strain at a point on the bracket due to the load P has components of ε x = 500 × 10 − 6 , ε y = 350 × 10 − 6 , and γ x y = − 430 × 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 500 × 10 − 6 for ε x , 350 × 10 − 6 for ε y , − 430 × 10 − 6 for γ x y , and − 30 ° for θ . ε x ′ = [ ( 500 × 10 − 6 ) + ( 350 × 10 − 6 ) 2 + ( 500 × 10 − 6 ) − ( 350 × 10 − 6 ) 2 cos 2 ( − 30 ° ) + ( − 430 × 10 − 6 ) 2 sin 2 ( − 30 ° ) ] = ( 425 × 10 − 6 ) + ( 75 × 10 − 6 × 0.5 ) − ( 215 × 10 − 6 × ( − 0.866 ) ) = 649 × 10 − 6 Hence, the normal strain component in x ′ direction is 649 × 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 500 × 10 − 6 for ε x , 350 × 10 − 6 for ε y , − 430 × 10 − 6 for γ x y , and − 30 ° for θ . ε y ′ = [ ( 500 × 10 − 6 ) + ( 350 × 10 − 6 ) 2 − ( 500 × 10 − 6 ) − ( 350 × 10 − 6 ) 2 cos 2 ( − 30 ° ) − ( − 430 × 10 − 6 ) 2 sin 2 ( − 30 ° ) ] = ( 425 × 10 − 6 ) − ( 75 × 10 − 6 × 0

Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (5th Edition)

5th Edition

ISBN: 9780134301006

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 14.8, Problem 94P

To determine

Find the equivalent in-plane strains on an element.

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.8, Problem 93P

Chapter 14.8, Problem 95P

Students have asked these similar questions

Hints: Find the closed loop transfer function and then plot the step response for diFerentvalues of K in MATLAB. Show step response plot for different values of K. Auto Controls Show solutions and provide matlab code NO COPIED ANSWERS OR WILL REPORT!!!! Use own solution

what is shear stress and normal? how to tell them while calculating?

12 mm 45 mm 20 kN 20 kN 12 mm 45 mm PROBLEM 1.61 For the assembly and loading of Problem 1.60, determine (a) the average shearing stress in the pin at C, (b) the average bearing stress at C in member BC, (c) the average bearing stress at B in member BC. PROBLEM 1.60 Two horizontal 20-kN forces are applied to pin B of the assembly shown. Knowing that a pin of 20-mm diameter is used at each connection, determine the maximum value of the average normal stress (a) in link AB, (b) in link BC.

Chapter 14 Solutions

Statics and Mechanics of Materials Plus Mastering Engineering with Pearson eText - Access Card Package (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 within the x-y plane.

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 within the x-y plane.

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 within the x-y plane.