Chapter 3, Problem 3.1P

Classify each of the following trusses as statically determinate, statically indeterminate, or unstable. If indeterminate, state its degree.

To determine

(a)

If, the truss is statically determinate, statically indeterminate or unstable and its degree.

Answer to Problem 3.1P

The truss is statically determinate.

Explanation of Solution

Given:

One end of the truss has roller support and the other end has pinned support.

Concept Used:

The determinacy of the structure is obtained from the formula:

   $\begin{array}{l}2\text{j=m+r}\\ \text{Degree of indeterminacy i=(m+r)-2j}\end{array}$

If $\text{i=0}$ then the truss is just statically determinate.

If $\text{i>0}$ then the truss is statically indeterminate.

If $\text{i<0}$ then the truss is unstable.

Where j is the number of joints.

m is the number of members of the truss.

r is the number of reactions at the support.

In case of pinned support there are two reactions.

In case of roller support there is only one reaction.

In case of fixed support there are three reactions.

In case of simple support there is only one reaction.

Calculation:

Here,

   $\begin{array}{l}\text{j=6}\\ \text{m=9}\\ \text{r=3}\\ \text{2j=12}\\ \text{m+r=12}\\ \text{i=(m+r)-2j}\\ \text{i=12-12=0}\end{array}$

Which implies that the truss is statically determinate.

Conclusion:

Hence, the truss is statically determinate.

To determine

(b)

If, the truss is statically determinate, statically indeterminate or unstable and its degree if indeterminate.

Answer to Problem 3.1P

The truss is statically indeterminate.

Degree of indeterminacy i=2.

Explanation of Solution

Given:

Both the ends of the truss have pinned joint.

Concept Used:

The determinacy of the structure is obtained from the formula:

   $\begin{array}{l}2\text{j=m+r}\\ \text{Degree of indeterminacy i=(m+r)-2j}\end{array}$

If $\text{i=0}$ then the truss is just statically determinate.

If $\text{i>0}$ then the truss is statically indeterminate.

If $\text{i<0}$ then the truss is unstable.

Where j is the number of joints.

m is the number of members of the truss.

r is the number of reactions at the support.

In case of pinned support there are two reactions.

In case of roller support there is only one reaction.

In case of fixed support there are three reactions.

In case of simple support there is only one reaction.

Calculation:

Here,

   $\begin{array}{l}\text{j=6}\\ \text{m=10}\\ \text{r=4}\\ \text{2j=12}\\ \text{m+r=14}\\ \text{i=(m+r)-2j}\\ \text{i=14-12=2}\end{array}$

Which implies that the truss is statically indeterminate with degree of indeterminacy as 2.

Conclusion:

Truss is statically indeterminate.

Degree of indeterminacy i=2.

To determine

(c)

If, the truss is statically determinate, statically indeterminate or unstable. If statically indeterminate and its degree.

Answer to Problem 3.1P

The truss is statically determinate.

Explanation of Solution

Given:

One end of the truss has pinned support and the other end has roller support.

Concept Used:

The determinacy of the structure is obtained from the formula:

   $\begin{array}{l}2\text{j=m+r}\\ \text{Degree of indeterminacy i=(m+r)-2j}\end{array}$

If $\text{i=0}$ then the truss is just statically determinate

If $\text{i>0}$ then the truss is statically indeterminate

If $\text{i<0}$ then the truss is unstable

Where j is the number of joints

m is the number of members of the truss

r is the number of reactions at the support

In case of pinned support there are two reactions

In case of roller support there is only one reaction

In case of fixed support there are three reactions

In case of simple support there is only one reaction

Calculation:

Here,

   $\begin{array}{l}\text{j=8}\\ \text{m=13}\\ \text{r=3}\\ \text{2j=16}\\ \text{m+r=16}\\ \text{i=(m+r)-2j}\\ \text{i=16-16=0}\end{array}$

Which implies that the truss is statically determinate.

Conclusion:

Truss is statically determinate.