A simple triangular roof truss ABC is pinned at A and supported by a roller at B. The span AB is $4\text{ m}$ long, and the height of the peak C is $2\text{ m}$. A downward load of $10\text{ kN}$ is applied at the peak C. Determine the force in member AC using the Method of Joints. Assume symmetry where applicable.

A Howe truss has a vertical load of $20\text{ kN}$ applied at the lower central joint. To find the internal force in the top horizontal member near the center, an engineer cuts a section through three members. If the moment about the cut's lower intersection point is $60\text{ kN}\cdot\text{m}$ from the external reactions, and the height of the truss is $3\text{ m}$, what is the force in the top member?

An A-frame ladder consists of two legs pinned at the top and connected by a horizontal tie rod halfway down. A person weighing $800\text{ N}$ stands exactly at the top pin. The ladder stands on a frictionless floor. Determine the tension in the horizontal tie rod.

During the visual inspection of a complex bridge truss, a junior engineer notices several diagonal members that appear to carry no load under the dead weight of the structure. They suggest removing them to save weight and material. Explain the concept of zero-force members and why removing them might be catastrophic.

A designer is choosing between a truss and a rigid frame for a warehouse roof. Explain the fundamental mechanical difference in how these two structures transfer loads and the implications for the joints used in their construction.