Chapter 4, Problem 1P

(a)

To determine

Categorize the given plane truss as unstable, statically indeterminate or statically determinate.

Find the degree of static indeterminacy in case the given truss is statically indeterminate.

Answer to Problem 1P

The given truss is unstable.

Explanation of Solution

Given information:

The Figure of plane truss is shown.

Calculation:

Show the conditions for plane truss as follows:

$\begin{array}{l}m+r<2j\text{the truss is statically unstable}\\ m+r=2j\text{the truss is statically determinate}\\ m+r>2j\text{the truss is statically indeterminate}\end{array}\}$        (1)

Here, m is the number of members of the truss, r is the support reactions and j is the number of joints.

Refer the Figure of the given plane truss.

The number of the members in the plane truss is $m=2$.

The number of reaction is $r=3$.

The number of the joints in the plane truss is $j=3$.

Substitute the values of m, r, and j with Equation (1).

$\begin{array}{l}m+r<2j\\ 2+3<2\times 3\\ 5<6\end{array}$

Thus, the plane truss is unstable.

(b)

To determine

Categorize the given plane truss as unstable, statically indeterminate or statically determinate.

Find the degree of static indeterminacy in case the given truss is statically indeterminate.

Answer to Problem 1P

The given truss is statically determinate.

Explanation of Solution

Given information:

The Figure of plane truss is shown.

Calculation:

Refer the Figure of the given plane truss.

The number of the members in the plane truss is $m=3$.

The number of reaction is $r=3$.

The number of the joints in the plane truss is $j=3$.

Substitute the values of m, r, and j with Equation (1).

$\begin{array}{l}m+r=2j\\ 3+3=2\times 3\\ 6=6\end{array}$

Thus, the plane truss is statically determinate.

(c)

To determine

Categorize the given plane truss as unstable, statically indeterminate or statically determinate.

Find the degree of static indeterminacy in case the given truss is statically indeterminate.

Answer to Problem 1P

The given truss is statically determinate.

Explanation of Solution

Given information:

The Figure of plane truss is shown.

Calculation:

Refer the Figure of the given plane truss.

The number of the members in the plane truss is $m=2$.

The number of reaction is $r=4$.

The number of the joints in the plane truss is $j=3$.

Compare the values of m, r, and j with Equation (1).

$\begin{array}{l}m+r=2j\\ 2+4=2\times 3\\ 6=6\end{array}$

Thus, the plane truss is statically determinate.

(d)

To determine

Categorize the given plane truss as unstable, statically indeterminate or statically determinate.

Find the degree of static indeterminacy in case the given truss is statically indeterminate.

Answer to Problem 1P

The given truss is unstable.

Explanation of Solution

Given information:

The Figure of plane truss is shown.

Calculation:

Refer the Figure of the given plane truss.

The number of the members in the plane truss is $m=3$.

The number of reaction is $r=4$.

The number of the joints in the plane truss is $j=4$.

Substitute the values of m, r, and j with Equation (1).

$\begin{array}{l}m+r<2j\\ 3+4<2\times 4\\ 7<8\end{array}$

Thus, the plane truss is unstable.