Principal stresses and the angle of plane in the beam at

Question

1: The cantilevered beam is subjected to the load at its end shown in figure below.

Determine:

a) Principal stresses and the angle of plane in the beam at point A & B by analytical method.

b) Principal stresses and the angle of plane in the beam at point A & B by graphical method.(Construct Mohr'sCircle)

 

2. The shaft is supported at A by a journal bearing that exerts only vertical reaction on theShaftand at B by a thrust bearing that exerts both horizontal and vertical reactions on the shaft, draw the bending momentdiagram for the shaft and then from this diagram sketch the deflection or elastic curve for the shaft's centre line.

Determine: The deflection at x₁ = x₂ = 100mm and assume E= 200 GPa and diameter of the shaft is 20 mm, as shown in the figure below

 

3. The steel bar AB has rectangular cross section. If it is pin connected at its ends, Determine: The maximum allowable intensity 'w' of the distributed load that can be applied to BC without causing the bar AB to buckle. Use factor of safety with respect to buckling F.S.= 1.5, Est =200 GPa, σy= 360 MPa.

Answer 1

Q1. The cantilevered beam is subjected to the load at its end illustrated in the figure below. Find out: a) Main stresses and the angle of plane in the beam at point A and B by analytical method. b) Main stresses and the angle of plane in the beam at point A and B by graphical method. Q2. The shaft is supported at A via a journal bearing which applies only vertical reaction on the Shaft and at B via a thrust bearing that applies both horizontal and vertical reactions on the shaft, draw the bending moment diagram for the shaft and then from this diagram draw the deflection or elastic curve for shaft's centre line. Find out deflection at x1 = x2 = 100mm and suppose E = 200 GPa and diameter of the shaft is 20 mm, as illustrated in the figure below.