A beam of length /= 1m, which is clamped at both ends, is modelled using four flexural elements. The first modeshape of the beam is described by:20.5443.0451.0000.0000.544- 3.045Note that Y₁ = ₁=Y₁ = =0 due to the boundary conditions. Recalling that displacement of a flexural element is given by:0y=S₁₂(x) y₂ +S₂(x) @ + S₂(x) y₂ + S₂(x) O111/22where the shape functions are given by:2$, (x) = 1 - 3 ( - ) ²+ ² ( ² ) ³*+2x3$₂(x)=x- 2 + ² + + ²2L L²x$₂(x) = ³ ( 7 ) * - 2 ( ² ) ³+2 x35(x) = -1/ 2 + + 20S₂(x)LL²Find the displacement of the first modeshape at position x=//8. Express your answer to three decimal places and do not include units in your answer.

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A beam of length /= 1m, which is clamped at both ends, is modelled using four flexural elements. The first modeshape of the beam is described by: O e O 0.544 3.045 1.000 0.000 0.544 -3.045 Note that Y₁ = ₁=Y₁ == 0 due to the boundary conditions. Recalling that displacement of a flexural element is given by: 1 1 5 5 y=S₂(x) y₂ +S₂(x) + S₂(x) y₂ + ₂(x) ₂ O 1 2 where the shape functions are given by: $₁(x) = 1-3 ( ² ) ² + 2 (²) ² S₂(x)=x-2-² +²2 L L2 $₂(x) = 3 ( ² ) ² - ² (+) ² x² x3 + S₂(x)=-I L² Find the displacement of the first modeshape at position x=//8. Express your answer to three decimal places and do not include units in your answer.

A beam of length /= 1m, which is clamped at both ends, is modelled using four flexural elements. The first modeshape of the beam is described by: O e O 0.544 3.045 1.000 0.000 0.544 -3.045 Note that Y₁ = ₁=Y₁ == 0 due to the boundary conditions. Recalling that displacement of a flexural element is given by: 1 1 5 5 y=S₂(x) y₂ +S₂(x) + S₂(x) y₂ + ₂(x) ₂ O 1 2 where the shape functions are given by: $₁(x) = 1-3 ( ² ) ² + 2 (²) ² S₂(x)=x-2-² +²2 L L2 $₂(x) = 3 ( ² ) ² - ² (+) ² x² x3 + S₂(x)=-I L² Find the displacement of the first modeshape at position x=//8. Express your answer to three decimal places and do not include units in your answer.

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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Graphical Methods

The graphical method is a method of solving equations involving more than one variable using the Cartesian coordinate system. In civil engineering, the use of the graphical method is limited to the problems involving two variables. The graphical method has a great impact in solving the questions regarding engineering mechanics.

Question

A beam of length /= 1m, which is clamped at both ends, is modelled using four flexural elements. The first modeshape of the beam is described by:
2
0.544
3.045
1.000
0.000
0.544
- 3.045
Note that Y₁ = ₁=Y₁ = =0 due to the boundary conditions. Recalling that displacement of a flexural element is given by:
0
y=S₁₂(x) y₂ +S₂(x) @ + S₂(x) y₂ + S₂(x) O
1
1
1/2
2
where the shape functions are given by:
2
$, (x) = 1 - 3 ( - ) ²+ ² ( ² ) ³*
+2
x3
$₂(x)=x- 2 + ² + + ²2
L L²
x
$₂(x) = ³ ( 7 ) * - 2 ( ² ) ³
+2 x3
5(x) = -1/ 2 + + 20
S₂(x)
L
L²
Find the displacement of the first modeshape at position x=//8. Express your answer to three decimal places and do not include units in your answer.

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