Module 2: Stability and Determinacy - Examples

A planar beam is supported by three vertical rollers. Determine whether the support arrangement is externally stable against arbitrary planar loading.

Three independent reaction forces in a planar model all pass through one point. Explain the instability.

A stable planar truss has $m=15$ members, $j=9$ joints, and a pin-and-roller support system giving $r=3$. Determine its static indeterminacy.

A stable planar truss has $m=18$, $j=10$, and $r=3$. Find the degree of static indeterminacy.

A planar pin-jointed assembly has $m=10$, $j=8$, and $r=3$. Evaluate the count.

A stable single-bay, single-story rigid portal frame has $m=3$ members, $j=4$ joints, and two fixed bases giving $r=6$. Take $c=0$. Determine $D_s$.

A stable planar rigid frame has $m=5$, $j=6$, $r=6$, and one independent internal moment release represented by $c=1$. Determine the static indeterminacy.

A planar frame model has three unconstrained joints. Each joint would normally have $u_x$, $u_y$, and $\theta_z$, but one joint is restrained against vertical translation and another has a prescribed zero rotation. Count the remaining active generalized coordinates.