Learning Goal:

Influence lines are constructed using a dimensionless unit load Therefore, the value of the function for any concentrated force $F$ can be found by multiplying the ordinate of the influence line at the position $x$ by the magnitude of $F.$ The location of concentrated load that will produce a maximum value of a function $($reaction$,$ shear, or moment$)$ corresponds to the maximum influence ordinate.

Influence lines can also be used to find values of a beam that is subjected to a distributed loading. The value of a function caused by a uniform distributed load is equal to the area under the influence line multiplied by the intensity of the uniform load. For maximum positive $($or negative$)$ reaction, shear, or moment, a distributed live load should cover the regions of the beam where the sign of the influence is positive $($or negative$).$ Furthermore, from the influence line, one can determine the location of a live load that will produce the maximum value of a function.

Figure

$1$ of $1$

The beam shown in $($Figure $1)$ is used to support a hoist that transfers large items to various points underneath it$.$ The max load the hoist can move is $P=45kN.$ The beam has a weight of $0\mathrm{.}80k\frac{N}{m}$ and is subjected to a uniform live load of $10\mathrm{.}9k\frac{N}{m}$ Assume the hoist has negligible size and weight, and can travel the entire leng of the beam. Also, assume $B$ is a pin and $D$ is a roller. Use this information to answer Parts A though $C$ below

Part A $-$ Maximum reaction at $D$

Part B $-$ Maximum shear at $C$

Part C $-$ Maximum moment at $C$

Determine the maximum moment in the beam at point $C$

Express your answer in $kN*m$ to three significant figures.

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