Question

A weight having a mass of 500 kg slides without friction down a 10-mm diameter steel rod 1 meter long through a distance of 10 mm. It is supported by a head fixed to the rod. (figure to be assigned in the class).

Determine:
The stress and the deflection in the rod under static conditions. That is, the weight is gradually lowered without impact until it comes to rest.

Answer 1

To determine the stress and deflection in the rod, we need to calculate the force acting on the rod and use the formulas for stress and deflection.

Step-by-step explanation:

In order to determine the stress and deflection in the rod, we need to first calculate the force acting on the rod and then use the formulas for stress and deflection.

The force acting on the rod is equal to the weight of the mass, which is given as 500 kg. The weight can be calculated using the formula W = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).

The stress can be calculated using the formula stress = F / A, where F is the force and A is the cross-sectional area of the rod. The cross-sectional area can be calculated using the formula A = πr², where r is the radius of the rod (half the diameter).

The deflection can be calculated using the formula deflection = (F * L) / (E * A), where F is the force, L is the length of the rod, E is the modulus of elasticity of the material, and A is the cross-sectional area of the rod.