Deflection of a uniform beam Figure 3(a) shows a uniform beam subject to a linearly increasing distributed load. The equation for the resulting elastic curve is (see Fig. 3(b)): •(-x5+2L²x³ - L^x) y = Wo 120EIL Use bisection method to determine the point of maximum deflection (i.e., the value of x where dy/dx = 0). Then substitute this value into the above equation to determine the value of the maximum deflection. Use the following parameter values in your computation: L = 600 cm, E = 50,000 kN/cm², I = 30,000 cm², and wo = 2.5 kN/cm. (x = 0, y = 0) (0) Wo (x = 1, y = 0) (b) Fig. 3: Deflection of a uniform beam.

Deflection of a uniform beam Figure 3(a) shows a uniform beam subject to a linearly increasing distributed load. The equation for the resulting elastic curve is (see Fig. 3(b)): •(-x5+2L²x³ - L^x) y = Wo 120EIL Use bisection method to determine the point of maximum deflection (i.e., the value of x where dy/dx = 0). Then substitute this value into the above equation to determine the value of the maximum deflection. Use the following parameter values in your computation: L = 600 cm, E = 50,000 kN/cm², I = 30,000 cm², and wo = 2.5 kN/cm. (x = 0, y = 0) (0) Wo (x = 1, y = 0) (b) Fig. 3: Deflection of a uniform beam.

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

Design of structures using FEA

An arrangement, in which various members are interconnected with their constrained relative motion, the whole arrangement is then known as a structure. The degree of freedom of such a structure is zero. In such a structure, the load can act throughout the length of the structure or at the joints.

Question

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For all the following problems,
3.
a)
b)
You need to show at least 3 iterations calculated manually with all steps.
You do not need to include the M.files for the bisection method (bisect.m) and for false position (falspos.m). You
must, however, show the command lines for the given functions with their variables and other parameters.
Deflection of a uniform beam
Figure 3(a) shows a uniform beam subject to a linearly increasing distributed load. The equation
for the resulting elastic curve is (see Fig. 3(b)):
-(-x5 + 2L²x³ - L^x)
y =
Wo
120EIL
Use bisection method to determine the point of maximum deflection (i.e., the value of x where dy/dx
Then substitute this value into the above equation to determine the value of the maximum deflection.
Use the following parameter values in your computation: L = 600 cm, E = 50,000 kN/cm²,
I = 30,000 cm4, and wo = 2.5 kN/cm.
(x = 0, y = 0)
(a)
Wo
(x = L₁y = 0)
(b)
Fig. 3: Deflection of a uniform beam.
X
=
0).

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