Objectives

To study methods for computing ultimate strength design forces and moments.

To review structural mechanics for developing beam forces.

To review applying the live load in strategic locations to produce the maximum responses $($reactions$,$ shears and moments$).$

Given:

The cantilevered beam with a uniform load, $w,$ and two concentrated loads, $P_1$ and $P_2$ at the locations shown below.

Concrete unit weight $=150pcf$

Beam width $=15",$ beam depth $=26"$

Unfactored uniform dead load, $w_D=1\mathrm{.}3\frac{k}{f}t($does not include self$-$weight$),$ unfactored uniform live load, $w_L=2\mathrm{.}4\frac{k}{f}t.$

Unfactored concentrated dead load $P_{lD}=2\mathrm{.}3$ kips, unfactored concentrated live load $P_{IL}=1\mathrm{.}9$ kips.

Unfactored concentrated dead load $P_{2D}=2\mathrm{.}6$ kips, unfactored concentrated live load $P_{2L}=2\mathrm{.}3$ kips.

Find:

Using the load combination $1\mathrm{.}2D+1\mathrm{.}6L,$ compute the following $($be sure to include the beam self$-$weight$)$:

Compute the maximum ultimate reactions at supports $"A"$ and $"B".$

Compute the maximum ultimate shear $(V_u)$ anywhere along the beam.

Compute the maximum ultimate positive and negative moments, and $($:$-M_u$