Problem: Compute for the vertical deflection at point C support B using either of the following method: a. Double Integration Method, b. Moment Distribution Method, c. Conjugate Beam Method, d. Virtual Work Method, or e. Castigliano's Theorem. El is constant. CHOOSE ONLY ONE METHOD TO US P A L 2 2

Problem: Compute for the vertical deflection at point C support B using either of the following method: a. Double Integration Method, b. Moment Distribution Method, c. Conjugate Beam Method, d. Virtual Work Method, or e. Castigliano's Theorem. El is constant. CHOOSE ONLY ONE METHOD TO US P A L 2 2

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

Problem: Compute for the vertical deflection at point C and
support B using either of the following method:
a. Double Integration Method,
b. Moment Distribution Method,
c. Conjugate Beam Method,
d. Virtual Work Method, or
e. Castigliano's Theorem.
El is constant. CHOOSE ONLY ONE METHOD TO USE.
C
B
L
2
(O

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Problem: Compute for the vertical deflection at point C and support B using either of the following method: a. Double Integration Method, b. Moment Distribution Method, c. Conjugate Beam Method, d. Virtual Work Method, or e. Castigliano's Theorem. El is constant. CHOOSE ONLY ONE METHOD TO USE. C В L L 2 2
2. By the moment-area method or conjugate-beam method, determine the deflection at the midspan (ElA) for the beam shown in figure below. All figures must be included and drawn straight. (Solve the deflection in terms of EI, these two values of E and I are not given in the problem.) P, P2 3.0m 1.0m 1.0m A 5.0m P1 P2 N N 976 676
Please solve fully with diagrams as needed and for all parts of the question. Question: a) What is deflected shape of the beam? b) Find dispacement of beam at point B using moment-area method. c) Find displacement of beam at point B using Castiglianos theorem. Assume EI is constant for all
Using the virtual work method determine slope of the beam at "A". Beam is subjected to a uniformly Distributed Load “W" and a concentrated moment "WL^2" at “A" (Express the results in terms of W, L, and EI) w ikIft=constant)
2. By the moment-area method or conjugate-beam method, determine the deflection at the midspan (EIA) for the beam shown in figure below. All figures must be included and drawn straight. (Solve the deflection in terms of El, these two values of E and I are not given in the problem.) P, P2 1.0m B 3.0m 1.0m A 5.0m P2 N 976 676
(a) Derive the equations for deflection of the beam segment BC and AB the following beam by the double integration method. (b) Locate the point of maximum deflection in BC and compute its magnitude. (Hint : derive the deflection equation for BC first).
Using Castigliano’s theorem. For the simply supported beam shown in the figure, determine the slope and deflection at point B.
Considering the solution above, can you help with part (d) 3. The beam shown below has a Young’s modulus of 50 GPa and has a square cross-section of side1 cm. Determine the following using the second-order integration method:(a) Bending moment M(x) along the length of the beam.(b) The slope of the beam θ(x).(c) The deflection of the beam v(x).(d) Slope of the beam at support θB
BP1: A cantilevered beam of constant EI and length L has a rectangular distributed load q over its length. Use integration method to find deflection. Begin at M(x) and proceed to y(x). A)Solve the deflection of the free end left to right B)Solve again but right to left