Chapter 7, Problem 7.3.1P

To determine

(a)

If all the spacing and edge distance requirements are adequate.

Answer to Problem 7.3.1P

The spacing and the edge distance provided are adequate.

Explanation of Solution

Given:

Tension member is $\text{PL}\frac{1}{2}\times 6$.

Thickness of the gusset plate is $\frac{3}{8}\text{inch}$.

Diameter of the bolts is $\frac{7}{8}\text{inch}$.

Steel Used is $\text{A36}$.

Calculation:

The properties for $\text{A}36$ steel from the AISC steel table are as follows:

The ultimate tensile stress is $58\text{ksi}$.

Write the expression for minimum spacing.

$S_{\text{m}}=\frac{8}{3}d$ ...... (I)

Here, diameter of the bolt is $d$ and minimum spacing is $S_{\text{m}}$.

Substitute $\frac{7}{8}\text{inch}$ for $d$ in Equation (I).

$\begin{array}{c}{S}_{\text{m}}=\frac{8}{3}\left(\frac{7}{8}\text{inch}\right)\\ =2.33\text{inch}\end{array}$

$$

The minimum spacing between the bolts is $2.33\text{inch}$ which is less than the actual spacing between the bolts, that is $2.75\text{inch}$. Therefore, the spacing is adequate.

For the edge distance to be adequate, the value of edge distance should be greater than or equal to the value of minimum edge distance.

$l_{\text{e}}\ge l_{\text{m}}$

Here, edge distance is $l_{\text{e}}$ and minimum edge distance is $l_{\text{m}}$.

The value of edge distance is $1.5\text{inch}$ and the value of minimum edge distance is $1.5\text{inch}$, which are equal. Therefore, the edge distance provided is adequate.

Conclusion:

Thus, the spacing and the edge distance provided are adequate.

To determine

(b)

The nominal bearing strength of each bolt.

Answer to Problem 7.3.1P

The nominal bearing strength of the edge bolt is $26.91\text{kips}$ and the nominal bearing strength for inner bolts is $45.68\text{kips}$.

Explanation of Solution

Calculation:

Write the expression for nominal bearing strength of a bolt.

$R_{\text{n}}=1.2l_{\text{c}}t{F}_{\text{u}}$ ...... (II)

Here, the nominal bearing strength is $R_{\text{n}}$, thickness is $t$, ultimate tensile stress is $F_{\text{u}},$ and the distance between the edge of the adjacent hole to the edge of the bolt hole is $l_{\text{c}}$.

With the upper limit of nominal bearing strength of the bolt,

$R_{\text{n}}=2.4dt{F}_{\text{u}}$

Write the expression to calculate the value of $l_{\text{c}}$ for edge bolts.

$l_{\text{c}}=l_{\text{e}}-\frac{h}{2}$ ...... (III)

Here, height of the bolt is $h$.

Write the expression to calculate the value of $l_{\text{c}}$ for inner bolts.

$l_{\text{c}}=s-h$ ...... (IV)

Here, spacing between the bolts is $s$.

Write the expression to calculate the height of the bolt.

$h=d+\frac{1}{16}\text{inch}$ ...... (V)

Calculate the value of $h$.

Substitute $\frac{7}{8}\text{inch}$ for $d$ in Equation (V).

$\begin{array}{c}h=\frac{7}{8}\text{inch}+\frac{1}{16}\text{inch}\\ \text{=}\frac{15}{16}\text{inch}\end{array}$

Calculate the value of $l_{\text{c}}$ for edge bolts.

Substitute $1.5\text{inch}$ for $l_{\text{e}}$ and $\frac{15}{16}\text{inch}$ for $h$ in Equation (III).

$\begin{array}{c}{l}_{\text{c}}=1.5\text{inch}-\frac{\left(\frac{15}{16}\text{inch}\right)}{2}\\ =1.031\text{inch}\end{array}$

Calculate the nominal bearing strength for edge bolts.

Substitute $1.031\text{inch}$ for $l_{\text{c}}$, $\frac{3}{8}\text{inch}$ for $t$ and $58\text{ksi}$ for $F_{\text{u}}$ in Equation (II).

$\begin{array}{c}{R}_{\text{n}}=1.2\left(1.031\text{inch}\right)\left(\frac{3}{8}\text{inch}\right)\left(58\text{ksi}\right)\\ =26.91\text{kips}\end{array}$

Calculate the upper limit of nominal bearing strength for edge bolts.

Substitute $\frac{7}{8}\text{inch}$ for $d$, $\frac{3}{8}\text{inch}$ for $t$ and $58\text{ksi}$ for $F_{\text{u}}$.

$\begin{array}{c}{R}_{\text{n}}=2.4\left(\frac{7}{8}\text{inch}\right)\left(\frac{3}{8}\text{inch}\right)\left(58\text{ksi}\right)\\ =45.68\text{kips}\end{array}$

Thus, the minimum value of $R_{\text{n}}$ is considered and is equal to $26.91\text{kips}$.

Calculate the value of $l_{\text{c}}$ for inner bolts.

Substitute $2.75\text{inch}$ for $s$ and $\frac{15}{16}\text{inch}$ for $h$ in Equation (IV).

$\begin{array}{c}{l}_{\text{c}}=2.75\text{inch}-\frac{15}{16}\text{inch}\\ =1.813\text{inch}\end{array}$

Calculate the nominal bearing strength for inner bolts.

Substitute $1.813\text{inch}$ for $l_{\text{c}}$, $\frac{3}{8}\text{inch}$ for $t$ and $58\text{ksi}$ for $F_{\text{u}}$ in Equation (II).

$\begin{array}{c}{R}_{\text{n}}=1.2\left(1.813\text{inch}\right)\left(\frac{3}{8}\text{inch}\right)\left(58\text{ksi}\right)\\ =47.32\text{kips}\end{array}$

Calculate the upper limit of nominal bearing strength for inner bolts.

Substitute $\frac{7}{8}\text{inch}$ for $d$, $\frac{3}{8}\text{inch}$ for $t$ and $58\text{ksi}$ for $F_{\text{u}}$.

$\begin{array}{c}{R}_{\text{n}}=2.4\left(\frac{7}{8}\text{inch}\right)\left(\frac{3}{8}\text{inch}\right)\left(58\text{ksi}\right)\\ =45.68\text{kips}\end{array}$

Thus, the minimum value of $R_{\text{n}}$ is considered and is equal to $45.68\text{kips}$.

Conclusion:

Thus, the nominal bearing strength of the edge bolt is $26.91\text{kips}$ and the nominal bearing strength for inner bolts is $45.68\text{kips}$.