Explanation Calculation: Show the free body diagram of the beam as in Figure 1. The beam and loading is symmetric. R C = R A Calculate the force ( F ) in the spring: F = 1 3 ( w ) ( 2 L ) = 2 3 w L Calculate the vertical reaction ( R A ) at point A by resolving the vertical component force. ∑ F y = 0 R A + F − w × ( 2 L ) + R C = 0 2 R A + ( 2 3 w L ) − w × ( 2 L ) = 0 R A = ( 4 3 w L ) 2 R A = R C = 2 3 w L Calculate the moment due to the reaction at A : M 1 = R A × L A B Here, L A B is length of the beam. Substitute 2 3 w L for R A and L for L A B . M 1 = 2 3 w L × L = 2 3 w L 2 Calculate the M 1 E I value: Substitute 2 3 w L 2 for M 1 . ( M 1 E I ) = 2 3 w L 2 E I = 2 w L 2 3 E I Show the ( M 1 E I ) diagram in below Figure 2. Calculate the area ( A 1 ) using the relation: A 1 = 1 2 ( L A B ) ( M 1 E I ) Substitute L for L A B and 2 w L 2 3 E I for ( M 1 E I ) . A 1 = 1 2 ( L ) ( 2 w L 2 3 E I ) = w L 3 3 E I Calculate the moment ( M 2 ) due the UDL: M 2 = − w × L × L 2 = − w L 2 2 Calculate the ( M 2 E I ) value: Substitute − w L 2 2 for M 2 . ( M 2 E I ) = − w L 2 2 E I = − w L 2 2 E I Show the ( M 2 E I ) diagram in below Figure 3

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

See similar textbooks

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

Videos

Question

Chapter 9.6, Problem 155P

To determine

The spring constant (k) for which the force in the spring is equal to one third of the total load on the beam.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.6, Problem 154P

Chapter 9.6, Problem 156P

Students have asked these similar questions

I need the answer as soon as possible

Parvinbhai

(a) Determine the maximum allowable horizontal span for a uniform cable with a weight per unit length of w if the tension in the cable is not to exceed a given value Tm. (b) Using the result of part a , determine the maximum span of a steel wire for which w = 0.25 lb/ft and Tm = 8000 lb.

Chapter 9 Solutions

EBK MECHANICS OF MATERIALS

Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - 9.1 through 9.4 For the loading shown, determine...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - Knowing that beam .AB is a W10 33 rolled shape...Ch. 9.2 - Knowing that beam AB is an S200 34 roiled shape...

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 spring constant ( k ) for which the force in the spring is equal to one third of the total load on the beam.

Solution Summary: The author shows the free body diagram of the beam as in Figure 1. The beam and loading is symmetric.

Concept explainers

Videos

The spring constant (k) for which the force in the spring is equal to one third of the total load on the beam.

Want to see the full answer?

Chapter 9 Solutions