Explanation Given information: The L-shaped frame is made from two segments, each of length L and flexural stiffness EI . Method adopted: Castigliano’s theorem. Explanation: Castigliano’s theorem to determine the slope for the beam is as follows: Δ = ∫ 0 L M ( ∂ M ∂ P ) d x E I (1) Here, Δ is displacement of the point caused by the real loads acting on the beam, P is an external force of variable magnitude applied to the beam at the point and in the direction of Δ , M is internal moment in the beam, expressed as a function of x and caused by both the force P and the actual loads on the beam, 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 ): Apply an external force P at the point where the displacement is to be determined. Region CB 0 ≤ x < L from top: Show the free body diagram of the beam for the region 0 ≤ x < L as in Figure 1. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x 1 = 0 M 1 − w × x 1 × x 1 2 = 0 (2) SolveEquation (2). M 1 = w ( x 1 ) 2 2 Region AB 0 < x ≤ L from point B : Show the free body diagram of the beam for the region 0 < x ≤ L as in Figure 2. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x 2 = 0 M 2 − w × L × L 2 + P ( x 2 ) = 0 (3) Solve Equation (3). M 2 = w L 2 2 − P x 2 Calculation: Tabulate the calculated values as in Table 1. Limit M ∂ M ∂ P M ( P = 0 ) 0 ≤ x < L M 1 = w ( x 1 ) 2 2 ∂ M 1 ∂ P = 0 M 1 = w ( x 1 ) 2 2 L < x ≤ 2 L M 2 = w L 2 2 − P x 2 ∂

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

Videos

Question

Chapter 14.10, Problem 14.143P

To determine

The vertical displacement of point B.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.10, Problem 14.142P

Chapter 14.10, Problem 14.144P

Students have asked these similar questions

-6- 8 من 8 Mechanical vibration HW-prob-1 lecture 8 By: Lecturer Mohammed O. attea The 8-lb body is released from rest a distance xo to the right of the equilibrium position. Determine the displacement x as a function of time t, where t = 0 is the time of release. c=2.5 lb-sec/ft wwwww k-3 lb/in. 8 lb Prob. -2 Find the value of (c) if the system is critically damping. Prob-3 Find Meq and Ceq at point B, Drive eq. of motion for the system below. Ш H -7~ + 目 T T & T тт +

Q For the following plan of building foundation, Determine immediate settlement at points (A) and (B) knowing that: E,-25MPa, u=0.3, Depth of foundation (D) =1m, Depth of layer below base level of foundation (H)=10m. 3m 2m 100kPa A 2m 150kPa 5m 200kPa B

W PE 2 43 R² 80 + 10 + kr³ Ø8=0 +0 R²+J+ kr200 R² + J-) + k r² = 0 kr20 kr20 8+ W₁ = = 0 R²+1) R²+J+) 4 lec 8.pdf Mechanical vibration lecture 6 By: Lecturer Mohammed C. Attea HW1 (Energy method) Find equation of motion and natural frequency for the system shown in fig. by energy method. m. Jo 000 HW2// For the system Fig below find 1-F.B.D 2Eq.of motion 8 wn 4-0 (1) -5- m

Chapter 14 Solutions

Mechanics of Materials

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 vertical displacement of point B .

Solution Summary: The author explains Castigliano's theorem to determine the slope for the beam.

Concept explainers

Videos

The vertical displacement of point B.

Want to see the full answer?

Chapter 14 Solutions