(a) To determine The principal strains. To sketch: The deformed element due to the principal strains. Explanation Given information: The strain rosette is attached at the point on the surface of the pump. The strain for each gage are ε a = − 250 × 10 − 6 , ε b = 300 × 10 − 6 , and ε c = − 200 × 10 − 6 . The angle of the gage are θ a = 0 ° , θ b = 60 ° , and θ c = − 60 ° . Calculation: Apply the strain transformation equations for the strain rosette as shown below. Find the normal strain in x direction as shown below. ε a = ε x cos 2 θ a + ε y sin 2 θ a + γ x y sin θ a cos θ a Here, ε x is the normal strain in the x direction, ε y is the normal strain in y direction, γ x y is the shear strain of the element, θ a is the angle of the gage a , and ε a , ε b , and ε c are the strain in gauges a , b , and c . Substitute − 250 × 10 − 6 for ε a and 0 ° for θ a . − 250 × 10 − 6 = ε x cos 2 0 ° + ε y sin 2 0 ° + γ x y sin 0 ° cos 0 ° ε x = − 250 × 10 − 6 Find the normal strain in y direction and shear strain of the element as shown below. For gauge b : ε b = ε x cos 2 θ b + ε y sin 2 θ b + γ x y sin θ b cos θ b Here, θ b is the angle of the gauge b . Substitute 300 × 10 − 6 for ε b , − 250 × 10 − 6 for ε x , and 60 ° for θ a . 300 × 10 − 6 = ( − 250 × 10 − 6 cos 2 60 ° ) + ( ε y sin 2 60 ° ) + γ x y sin 60 ° cos 60 ° 362.5 × 10 − 6 = 0.75 ε y + 0.433 γ x y 0.75 ε y + 0.433 γ x y = 362.5 × 10 − 6 (1) For gauge c : ε c = ε x cos 2 θ c + ε y sin 2 θ c + γ x y sin θ c cos θ c Here, θ c is the angle of the gauge c . Substitute − 200 × 10 − 6 for ε c , − 250 × 10 − 6 for ε x and − 60 ° for θ a . − 200 × 10 − 6 = [ − 250 × 10 − 6 cos 2 ( − 60 ° ) + ε y sin 2 ( − 60 ° ) + γ x y sin ( − 60 ° ) cos ( − 60 ° ) ] − 137.5 × 10 − 6 = 0.75 ε y − 0.433 γ x y 0.75 ε y − 0.433 γ x y = − 137.5 × 10 − 6 (2) Solve the Equations (1) and (2) to get ε y and γ x y . ε y = 150 × 10 − 6 γ x y = 577.37 × 10 − 6 Apply the procedure for the construction of Mohr’s circle as shown below. Find the centre of the circle C located ε avg = ε x + ε y 2 from the origin. Plot the reference points A having coordinates A ( ε x , γ x y 2 ) . This point represents the case when the x ′ axis coincides with the x axis. Hence, θ = 0 . Connect the point A with C and from the shaded triangle find the radius R of the circle. Sketch the circle using calculated R value. Construct the Mohr’s circle as shown below (b) To determine The maximum in-plane shear strain and average normal strain. To sketch: The deformed element due to the strains.

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 10.5, Problem 10.27P

(a)

To determine

The principal strains.

To sketch: The deformed element due to the principal strains.

(b)

To determine

The maximum in-plane shear strain and average normal strain.

To sketch: The deformed element due to the strains.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.5, Problem 10.26P

Chapter 10.5, Problem 10.28P

Students have asked these similar questions

I tried this problem a couple of times and don't know where I'm going wrong can you help me out please

y(0)=1, Using Laplace transforms solve the following differential equations : 11) y"-4y+4y=0, 12) y+2y+2y=0, y(0)=2.1, y'(0) = 3.9 y'(0)=-3. 13) y+7y+12y=21e", y(0)=3.5, y'(0)=-10. 14) +9y=10e. y(0)=0, y'(0) = 0. 15) y+3y+2.25y=91³ +64, y(0)=1, y'(0) = 31.5 16) -6y+5y= 29 cos(21), y(0)=3.2, y'(0)=6.2 17) "+2y+2y=0, y(0)=0, y'(0)=1. 18) +2y+17y=0, y(0)=0, y'(0)=12. 19) y-4y+5y=0, y(0)=1, y'(0) = 2. 20) 9y-6y+y=0, y(0)=3, y'(0)=1. 21) -2y+10y=0, y(0)=3, y'(0)=3.

4. Consider the rectangulan 2535 Let 16 a and section discussed 977b + class. in ie make a M thin" rectangle, Can you you show that Q = Go {a² = x² } . Imax = 2 Ga ты J =

Chapter 10 Solutions

MECHANICS OF MATERIALS-TEXT

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.