(a) Explanation Calculation: Use moment area method: Show the free body diagram of the beam as in Figure 1. Show the moment ( M E I ) diagram for the loading beam as in Figure 2. Due to symmetric beam with symmetric loading, consider the left side of the beam. Calculate the moment ( M ) using the formula: M = M 0 Calculate the ratio of M E I : Ratio = M E I Substitute M 0 for M . M E I = M 0 E I Calculate the area ( A ) due to the moment ( M ) using the formula: A = b h Here, b is the width of the triangle in area ( A ) and h is the height of the triangle in area ( A ). Substitute ( L 2 − a ) for b and M 0 E I for h . A = ( L 2 − a ) × ( M 0 E I ) = M 0 E I ( L − 2 a 2 ) = M 0 2 E I ( L − 2 a ) Show the tangent slope and deflection related to reference tangent as in Figure 3. Place the reference tangent at C then the slope ( θ C ) and deflection ( y C ) is zero respectively (b) To determine Find the deflection ( y C ) at point C .

7th Edition

ISBN: 8220100257063

Author: BEER

Publisher: YUZU

See similar textbooks

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and af…

Videos

Question

Chapter 9.5, Problem 113P

(a)

To determine

Find the slope (θA) at end A.

(b)

To determine

Find the deflection (yC) at point C.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 112P

Chapter 9.5, Problem 114P

Students have asked these similar questions

Problem 1 (30 Points) Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in both scenarios, there is one generalized coordinate, . R Scenario 1 R m R g Scenario 2 m HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the bowl (scenario 1), or the pivot point of the pendulum (scenario 2). Part I a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points) b) What can you say about the systems based on the Lagrangian? (2 points) c) Solve for the equations of motion for both systems. (8 points) Part II Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to determine the normal force acting on the mass. a)…

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)

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.

Find the slope ( θ A ) at end A .

Solution Summary: The author illustrates the moment area method by showing the free body diagram of the beam as in Figure 1.