Textbook Problem

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The roof system of an office building consists of a 4 in. thick reinforced concrete slab resting on four steel beams (A = 16.2 in.²), which are supported by two steel girders (A = 42.9 in²). The girders, in turn, are supported by four columns, as shown in Fig. P2.8. Determine the dead loads acting on the girder AG.

FIG. P2.8, P2.11

To determine

Find the dead load acting on the girder AG.

Explanation of Solution

Given information:

Consider the office building.

The thickness of the reinforced concrete slab is $4\text{in}\text{.}$.

Show the unit conversion of the thickness as follows:

$\begin{array}{l}t=4\text{in}\text{.}\times \frac{1\text{ft}}{12\text{in}\text{.}}\\ t=\frac{4}{12}\text{ft}\end{array}$

The area of the steel girder is $A_{sg}=42.9\text{in}{\text{.}}^2$.

Show the unit conversion of the area of the steel girder as follows:

$\begin{array}{c}{A}_{sg}=42.9\text{in}{\text{.}}^2\times \frac{1}{{12}^2\text{in}{\text{.}}^2}{\text{ft}}^2\\ =\text{0}\text{.29791}{\text{ft}}^2\end{array}$

The area of the steel floor is $A_{sf}=16.2\text{in}{\text{.}}^2$.

Show the unit conversion of the area of the steel girder as follows:

$\begin{array}{c}{A}_{sf}=16.2\text{in}{\text{.}}^2\times \frac{1}{{12}^2\text{in}{\text{.}}^2}{\text{ft}}^2\\ =\text{0}\text{.1125}{\text{ft}}^2\end{array}$

Calculation:

Refer Table 2.1: Unit Weight of the Construction Materials.

The unit weight of the structural steel is ${\gamma }_s=490{\text{lb/ft}}^3$.

The unit weight of the reinforced concrete is ${\gamma }_c=150{\text{lb/ft}}^3$.

Show the slab as shown in Figure 1.

Refer Figure 1.

Calculate the dead load on the steel girder as follows:

$\begin{array}{c}\text{Dead}\text{load on the steel girder}=\text{Unit weight of the steel}\times A_{Sg}\\ =490\times 0.2979\\ \approx 146\text{lb/ft}\end{array}$

Thus, the dead on the steel girder is $\underset{\_}{146\text{lb/ft}}$.

Show the tributary area of the column A and G as shown in Figure 2.

Refer Figure 1 and Figure 2.

Calculate the concentrated load at A and G as follows:

$\begin{array}{c}\left(\begin{array}{l}\text{Concentrated load }\\ \text{at }A\text{ and }G\end{array}\right)=\left(\begin{array}{l}\text{Load}\text{of the concrete slab in the shaded region at }A\text{or }G\\ +\text{Load of the floor beam in the shaded region}\text{at }A\text{or }G\end{array}\right)\\ =\left(150\times \frac{9}{2}\times \frac{20}{2}\times \frac{4}{12}\right)+(490\times 0\end{array}$