Figure Q1 shows a cantilever beam ABCDE subjected to a uniformly distributed load, w from points B to C. There are also a point load and a bending moment at points D and E, respectively. By using Macaulay's method; a) Develop the deflection equation in terms of w, L, E and I. Take point A as the origin. b) Given that El = 100×10° Nm² and L = 8m, determine the value of w so that the vertical deflection at point C is 2.5 mm. c) Then, develop the slope and deflection functions if a roller support is added at point E. Take w = 600 N/m.

Figure Q1 shows a cantilever beam ABCDE subjected to a uniformly distributed load, w from points B to C. There are also a point load and a bending moment at points D and E, respectively. By using Macaulay's method; a) Develop the deflection equation in terms of w, L, E and I. Take point A as the origin. b) Given that El = 100×10° Nm² and L = 8m, determine the value of w so that the vertical deflection at point C is 2.5 mm. c) Then, develop the slope and deflection functions if a roller support is added at point E. Take w = 600 N/m.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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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 after loading.

Question

1. Figure Q1 shows a cantilever beam ABCDE subjected to a uniformly distributed load, w
from points B to C. There are also a point load and a bending moment at points D and E,
respectively. By using Macaulay's method;
a) Develop the deflection equation in terms of w, L, E and I. Take point A as the origin.
b) Given that EI = 100×106 Nm? and L = 8m, determine the value of w so that the vertical
deflection at point C is 2.5 mm.
c) Then, develop the slope and deflection functions if a roller support is added at point E.
Take w = 600 N/m.
P=:
16
W
M=wL²
32
A
B
C
E
L/4
L/2
L/8
L/8
Figure Q1
[Ans: b) w = 601.44 N/m]

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