The vertical force P acts on the bottom of the plate having a negligible weight. Determine the shortest distance d to the edge of the plate at which it can be applied so that it produces no compressive stresses on the plate at section a-a. The plate has a thickness of 10 mm and P acts along the center line of this thickness.

200mm is the width and d is the distance from the right edge to the force P.

The shortest distance d to the edge of the plate is 66.67 mm

Concepts and reason

Moment of a force:

Moment of a force refers to the propensity of the force to cause rotation on the body it acts upon. The magnitude of the moment can be determined from the product of force’s magnitude and the perpendicular distance to the force.

Moment(M) = Force(F)×distance(d)

Moment of inertia ( I )

It is the product of area and the square of the moment arm for a section about a reference. It is also called as second moment of inertia.

First prepare the free body diagram of sectioned plate and apply moment equilibrium condition and also obtain area and moment of inertia of rectangular cross section. Finally, calculate the shortest distance using the formula of compressive stress (σ) in combination of axial and bending stress

Solution and Explanation:

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