Analysis of Simple Structures Examples

A triangular roof assembly has straight members pinned at their ends, and all loads are applied only at the joints. Should the elementary model be treated as an ideal truss or frame?

At unloaded joint $J$, members $JA$ and $JB$ are collinear while member $JC$ is non-collinear. There is no support reaction at $J$. Determine the force in $JC$.

At a symmetric apex joint, two identical rafters make $45^\circ$ with the horizontal and support a $20.0\ \text{kN}$ downward load. Determine the axial force magnitude in each rafter.

At joint $A$, a $12.0\ \text{kN}$ downward load acts. Member $AB$ is horizontal and member $AC$ rises at $30.0^\circ$ above the horizontal. Determine the two member forces, assuming tension away from the joint as positive.

You need only the force in one central chord member of a large planar truss. Explain how to choose an efficient section.

A cut truss segment has an unknown horizontal chord force $F$ located $2.00\ \text{m}$ above point $O$. All other cut-force lines pass through $O$. The external loads on the isolated side produce a net $+30.0\ \text{kN}\cdot\text{m}$ counterclockwise moment about $O$. Determine $F$ if its assumed direction produces a counterclockwise moment.

An ideal planar truss has $j=6$ joints, $m=9$ members, and a pin-plus-roller support system giving $r=3$. Check the count $m+r$ versus $2j$.

A roof member is rigidly connected at both ends and carries a distributed ceiling load along its span. Can it be modeled as a two-force truss member for that loading?

Exactly two non-collinear truss members meet at joint $K$. No external load or support reaction acts at the joint. Determine the member forces for this load case.

At a joint, member $JA$ is oriented $40.0^\circ$ above the positive $x$-axis and member $JB$ is oriented $30.0^\circ$ below the positive $x$-axis. A $20.0\ \text{kN}$ downward load acts at the joint. Assume both unknown member forces are tensile and directed away from the joint. Determine their signed values.

A section through a planar truss exposes a target horizontal member force $F$ whose line of action is $2.50\ \text{m}$ below point $O$. The other two cut-member force lines pass through $O$. External loads on the retained side create a net $-40.0\ \text{kN}\cdot\text{m}$ moment about $O$. The assumed target force produces a positive moment about $O$. Determine $F$.