Explanation Given information: The modulus of elasticity of the beam is E = 29 × 10 6 psi . The magnitude of applied load is P = 8 kips . The length of portion AD is L = 6 ft . The length of portion DB is a = 3 ft . Calculation: Calculate the moment of inertia of the beam as shown below. I = b d 3 12 Substitute 1.5 in . for b and 3 in . for d . I = 1.5 × 3 3 12 = 3.375 in . 4 Due to the symmetry of the beam, the reactions at supports B and C are Equal. R C = R C = P Sketch the Free Body Diagram as shown in Figure 1. Consider a section at a distance x from A over the portion AB . Due to the symmetry of the beam U A B = U C D . Take moment about the section is Equal to zero. ∑ M = 0 M + P x = 0 M = − P x Calculate the strain energy ( U A D ) over portion AD as shown below. U A D = ∫ a b M 2 2 E I d x (1) Substitute − P x for M and apply the limits in Equation (1). U A B = ∫ 0 a ( − P x ) 2 2 E I d x = 1 2 E I ∫ 0 a P 2 x 2 d x = P 2 2 E I ( x 3 3 ) 0 a = P 2 a 3 6 E I Hence, U E B = P 2 a 3 6 E I . The moment over portion BC is M = − P a . Calculate the strain energy ( U B C ) over portion BC as shown below. Substitute − P a for M and apply the limits in Equation (1). U B C = ∫ 0 b ( − P a ) 2 2 E I d x = 1 2 E I ∫ 0 b P 2 a 2 d x = P 2 a 2 2 E I ( x ) 0 b = P 2 a 2 b 2 E I Calculate the strain energy ( U ) of the prismatic beam as shown below

7th Edition

ISBN: 8220100257063

Author: BEER

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 11.3, Problem 29P

To determine

The strain energy due to bending for the steel beam.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 28P

Chapter 11.3, Problem 30P

Students have asked these similar questions

Consider 0.65 kg of N2 at 300 K, 1 bar contained in a rigid tank connected by a valve to another rigid tank holding 0.3 kg of CO2 at 300 K, 1 bar. The valve is opened and gases are allowed to mix, achieving an equilibrium state at 290 K. Determine: (a) the volume of each tank, in m³. (b) the final pressure, in bar. (c) the magnitude of the heat transfer to or from the gases during the process, in kJ. (d) the entropy change of each gas and of the overall system, in kJ/K.

(Read Image) (Answer: ω = 1.10 rad/sec CW)

What is the configuration of the control loop if steam must be shut down in case of a problem? (I found this question on the internet and was wondering what the answer is) A.Valve is fail open, PIC is direct-acting, TIC is reverse acting, and controller algorithm is feed-forwarding.B. Valve is fail open, PIC is reverse-acting, TIC is direct acting, and controller algorithm is cascade.C. Valve is fail closed, PIC is direct-acting, TIC is reverse acting, and controller algorithm is feed-forward.D. Valve is fail closed, PIC is reverse-acting, TIC is reverse acting, and controller algorithm is cascade.

Chapter 11 Solutions

EBK MECHANICS OF MATERIALS

Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - Prob. 7P Ch. 11.3 - Prob. 8P Ch. 11.3 - Using E = 29 106 psi, determine (a) the strain...Ch. 11.3 - Using E = 200 GPa, determine (a) the strain energy...

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 strain energy due to bending for the steel beam.

Solution Summary: The author explains the strain energy due to bending for the steel beam. The modulus of elasticity of the beam is E=29times 106

Videos

The strain energy due to bending for the steel beam.

Want to see the full answer?

Chapter 11 Solutions