Ladder as Working Platform

After watching a late night TV commercial about a folding extension ladder, Debbie thought she could use it to help her re-shingle her roof. The problem is she needs a flat surface to work on, but the roof has a slope of 38 degrees. However, this special folding extension ladder can pivot around the center joint which will allow it to be positioned on the roof as shown at the left.

Debbie, who is a structural engineer, is concerned that the joint will experience high loads and may fail.

What is known:

• The folding extension ladder has two legs, each are four feet long.
• Debbie, the person to work on the ladder, weighs 150 lbs.
• The roofing material will be stacked on the left side of the platform. The material weight is assumed to be a linear distributed loading as shown.
• There is a temporary support wood strip attached to the roof that stops the ladder from sliding. This boundary can be assumed to act like a fixed pin joint.
• The ladder pivot point is locked and will not rotate.
• The top leg rests on the roof. It is assumed that the roof is smooth (no friction).

What is the internal moment, shear force and axial force at point just to the left of the the central joint (section a-a)?

• Using static equilibrium equations, determine the boundary reaction.
• Cut the structure at section a-a and analyze either the left or right section by applying static equilibrium equations.
• Use the correct sign convention for cut surface.