Analysis of Statically Determinate Structures - Examples & Applications

Calculate the reactions and draw the Shear and Moment Diagrams for a simply supported beam of length $L=10\text{ m}$ with a single point load $P=20\text{ kN}$ located at the midspan ($x=5\text{ m}$).

Determine the internal axial force in each member of the equilateral truss ABC (where each side has length $L=4\text{ m}$). A vertical point load $P=10\text{ kN}$ acts downwards at the top joint B. The supports are a Pin at A and a Roller at C.

Find the force in member BC of a generic Pratt truss with a height $h=4\text{ m}$ and panel width $d=3\text{ m}$. A vertical point load of $20\text{ kN}$ is applied at the bottom chord joint D (which is 1 panel width from the left support). The total span is 4 panels ($12\text{ m}$). The left support A is a pin, and the right support E is a roller.

Calculate the internal forces (axial force $N$, shear force $V$, and bending moment $M$) at a section $C$ located in the middle of a continuous vertical column (member AB) of a 2D portal frame. A horizontal wind load of $P = 50\text{ kN}$ is applied at the top joint B. The frame has a pinned support at A and a roller support at D.

Determine the shear and bending moment equations as a function of $x$ for a cantilever beam of length $L=6\text{ m}$ subjected to a uniformly distributed load of $w=10\text{ kN/m}$ over its entire length. The beam is fixed at the left end ($x=0$).

Case Study: Analysis Strategy for a Compound Truss.

Case Study: Method of Substitute Members for a Complex Truss.