# Uniformly Distributed Load

## Example 01: Safe Uniform Load for a Beam that was Notched at the Tension Fibers at Supports

**Problem**

A 75 mm × 150 mm beam carries a uniform load *w _{o}* over the entire span of 1.2 m. Square notches 25 mm deep are provided at the bottom of the beam at the supports. Calculate the safe value of

*w*based on shear alone.

_{o}Allowable shear normal to grain = 1.85 MPa

## Influence Lines

Influence line is the graphical representation of the response function of the structure as the downward unit load moves across the structure. The ordinate of the influence line show the magnitude and character of the function.

The most common response functions of our interest are *support reaction*, *shear at a section*, *bending moment at a section*, and *force in truss member*.

With the aid of influence diagram, we can...

- determine the position of the load to cause maximum response in the function.
- calculate the maximum value of the function.

Value of the function for any type of load

$\displaystyle \text{Function} = \int_{x_1}^{x_2} y_i (y \, dx)$

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