a) Calculate the reaction forces in terms of F and theta. b) Calculate the internal shear force and moment as a function of x using cuts and summing forces and moments in terms of F, L, and theta. c) Calculate the shear force and moments by integration in terms of x, L, F and theta.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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a) Calculate the reaction forces in terms of F and
theta.
b) Calculate the internal shear force and moment as a function of x using cuts and summing
forces and moments in terms of F, L, and
theta.
c) Calculate the shear force and moments by integration in terms of x, L, F and
theta.
d) Assuming a rectangular cross section compute the average normal stress for the case F =10kN
at 30° where b =0.04 m, h = 0.08 m, at the point x = L/4, L = 1 m at the centroid.
e) With the cross section given above compute the average normal stress for the case F =10kN at
30° at the point x = L/4, L = 1 m at each surface of the beam.
f) Calculate the shear stress at the top and bottom surface, at the neutral axis and at x = 0.25 m
and y = 0.02 m above the neutral axis.

The image depicts a simple beam setup commonly used in structural analysis. The main components and labels in the diagram are as follows:

- The beam is horizontally positioned and supported at two points: a pin on the left and a roller on the right. This configuration allows the beam to rotate at the pin and to expand or contract longitudinally at the roller.

- The coordinate system is defined with axes labeled as \(x\) (horizontal) and \(y\) (vertical).

- The length of the beam is \(L\) meters, as indicated by the horizontal double-headed arrow.

- A force \(F\) is applied at an angle \(\theta\) from the horizontal axis, impacting the top side of the beam at its midpoint, \(L/2\).

- To the right, an "End view" is provided, showing a rectangle representing the cross-section of the beam, with width \(b\) and height \(h\).

This configuration and diagram are typically used to analyze the static equilibrium of beams, considering factors such as bending moments, shear forces, and deflection.
Transcribed Image Text:The image depicts a simple beam setup commonly used in structural analysis. The main components and labels in the diagram are as follows: - The beam is horizontally positioned and supported at two points: a pin on the left and a roller on the right. This configuration allows the beam to rotate at the pin and to expand or contract longitudinally at the roller. - The coordinate system is defined with axes labeled as \(x\) (horizontal) and \(y\) (vertical). - The length of the beam is \(L\) meters, as indicated by the horizontal double-headed arrow. - A force \(F\) is applied at an angle \(\theta\) from the horizontal axis, impacting the top side of the beam at its midpoint, \(L/2\). - To the right, an "End view" is provided, showing a rectangle representing the cross-section of the beam, with width \(b\) and height \(h\). This configuration and diagram are typically used to analyze the static equilibrium of beams, considering factors such as bending moments, shear forces, and deflection.
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