Chapter 2, Problem 2.1PFS

To determine

To find: maximum combined load for LRFD for a given loading $D=80\text{psf, }L=100\text{psf, }R=14\text{psf, }{L}_r=20\text{psf and }S=28\text{psf}$.

Answer to Problem 2.1PFS

$270\text{psf}$ .

Explanation of Solution

Given data:

$\begin{array}{l}D=80\text{psf}\\ L=100\text{psf}\\ R=14\text{psf}\\ L_r=20\text{psf}\\ S=28\text{psf}\end{array}$

Calculation:

Consider the dead load:

For the maximum combined load:

$Load=1.4D$

Substitute the value of D as $80\text{ psf}$ (as given in problem) in the formula

$\begin{array}{c}\because Load=1.4D\\ =1.4\left(80\right)\\ =112\text{psf}\end{array}$

Now, consider dead load, live load and snow load:

For the maximum combined load:

$Load=1.2D+1.6L+0.5S$

Substitute the values of D as $80\text{ psf}$, L as $100\text{ psf}$ and S as $28\text{ psf}$ in formula

$\begin{array}{c}Load=1.2D+1.6L+0.5S\\ =1.2\left(80\right)+1.6\left(100\right)+0.5\left(28\right)\\ =270\text{psf}\end{array}$

Now consider dead load, snow load and live load:

For the maximum combined load:

$Load=1.2D+1.6S+0.5L$

Substitute the values of D as $80\text{ psf}$, S as $28\text{ psf}$ and L as $100\text{ psf}$ in formula

$\begin{array}{c}Load=1.2D+1.6L+0.5S\\ =1.2\left(80\right)+1.6\left(28\right)+0.5\left(100\right)\\ =190.8\text{psf}\end{array}$

Now consider dead load, wind load, live load and snow load:

For the maximum combined load:

$Load=1.2D+1.0W+0.5L+0.5S$

Substitute the values of D as $80\text{ psf}$, W as $\text{0 psf}$, L as $100\text{ psf}$ and S as $28\text{ psf}$ in formula

$\begin{array}{c}Load=1.2D+1.0W+0.5L+0.5S\\ =1.2\left(80\right)+1.0\left(0\right)+0.5\left(100\right)+0.5\left(28\right)\\ =160\text{psf}\end{array}$

Now consider dead load and wind load:

For the maximum combined load:

$Load=0.9D+1.0W$

Substitute the values of D as $80\text{ psf}$, W as $\text{0 psf}$ in formula

$\begin{array}{c}Load=0.9D+1.0W\\ =0.9\left(80\right)+1.0\left(0\right)\\ =72\text{psf}\end{array}$

Now consider dead load, earthquake load, live load and snow load:

For the maximum combined load:

$Load=1.2D+1.0E+0.5L+0.2S$

Substitute the values of D as $80\text{ psf}$ ,E as $\text{0 psf}$ ,L as $100\text{ psf}$ and S as $28\text{ psf}$ in formula

$\begin{array}{c}Load=1.2D+1.0E+0.5L+0.2S\\ =1.2\left(80\right)+1.0\left(0\right)+0.5\left(100\right)+0.2\left(28\right)\\ =151.6\text{psf}\end{array}$

Now consider dead load and earthquake load:

For the maximum combined load:

$Load=0.9D+1.0E$

Substitute the values of D as $80\text{ psf}$ and E as $\text{0 psf}$ in formula

$\begin{array}{c}Load=0.9D+1.0E\\ =0.9\left(80\right)+1.0\left(0\right)\\ =72\text{psf}\end{array}$

Now look for the maximum value in all load combinations calculated earlier.

Conclusion:

The maximum load combination is dead load, live load and snow load with magnitude $270\text{psf}$.