Explanation Given information: EI is constant. Assumptions: Consider that the right side force as positive and left side as negative in horizontal components of forces. Consider that the upward force as positive and downward as negative in vertical components of forces. Consider that the clockwise moment as negative and anticlockwise moment as positive. Virtual-work equation for the entire beam as follows: 1 ⋅ Δ = ∫ 0 L m M E I d x (1) Here, 1 is external virtual unit load acting on the beam in the direction of Δ , Δ is displacement caused by the real loads on the beam, m is internal virtual moment in the beam, expressed as a function of x and caused by the external virtual unit load, M is internal moment in the beam, expressed as a function of x and caused by the real loads, E is modulus of elasticity of a member, and I is moment of inertia of the cross-sectional area about the neutral axis. Internal moment in the beam ( M ): Determine the reactions: Show the free-body diagram of the entire beam as in Figure 1. Moment about point A : Determine the vertical reaction at point B by taking moment about point A . ∑ M A = 0 B y ( L ) − 1 2 × w 0 × L 2 × 2 3 × L 2 − 1 2 × w 0 × L 2 × ( L 2 + 1 3 L 2 ) = 0 B y ( L ) − w 0 L 2 12 − w 0 L 4 × ( 4 L 6 ) = 0 B y ( L ) − w 0 L 2 12 − 2 w 0 L 2 12 = 0 B y = w 0 L 4 Along the vertical direction: Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 A y + B y − 1 2 × w 0 × L 2 − 1 2 × w 0 × L 2 = 0 (2) Substitute w 0 L 4 for B y in Equation (2). A y + w 0 L 4 − w 0 L 4 − w 0 L 4 = 0 A y = w 0 L 4 Region 0 ≤ x < L 2 : Show the free body diagram of the beam for the region 0 ≤ x < L 2 as in Figure 2. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x = 0 M − A y ( x ) + 1 2 × 2 w 0 L × x × x × 1 3 × x = 0 (3) Substitute w 0 L 4 for A y Equation (3). M 1 − w 0 L 4 ( x ) + w 0 ( x ) 3 3 L = 0 M 1 = w 0 L x 4 − w 0 ( x ) 3 3 L Internal virtual moment in the beam ( m ): Apply a unit loadat point C and calculate the moments

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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 14.7, Problem 14.112P

To determine

The displacement of the shaft C.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.7, Problem 14.111P

Chapter 14.7, Problem 14.113P

Students have asked these similar questions

please solve and show work

A thin plastic membrane separates hydrogen from air. The molar concentrations of hydrogen in the membrane at the innner and outer surfaces are determined to be 0.045 and 0.002 kmol/m^3 respectiveley. The binary diffusion coefficent of hydrogen in plastic at the operation temp is 5.3*10^-10 m^2/s. Determine the mass flow rate of hydrogen by diffusion through the membrane under steady conditions if the thickeness of the membrane is 2mm and 0.5 mm.

Chapter 14 Solutions

MECHANICS OF MATERIALS-TEXT

Ch. 14.2 - A material is subjected to a general state of...Ch. 14.2 - The strain-energy density for plane stress must be...Ch. 14.2 - 14–3. Determine the strain energy in the stepped...Ch. 14.2 - Prob. 14.4P Ch. 14.2 - Using bolts of the same material and...Ch. 14.2 - If P = 60 kN, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - *14–8. Determine the torsional strain energy in...Ch. 14.2 - Determine the torsional strain energy in the A-36...Ch. 14.2 - The shaft assembly is fixed at C. The hollow...

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 displacement of the shaft C .

Concept explainers

Videos

The displacement of the shaft C.

Want to see the full answer?

Chapter 14 Solutions