Answer to Question #256120 in Mechanical Engineering for hugh

Question

QUESTION 3 [ 17 Marks]

(a) Give the different types of loading and supports on a beam.

[7]

(b) State the assumptions made in the theory of pure bending.

[3]

(c) In a civil engineering construction site, a rectangular support beam 100 mm wide and

250 mm deep is exposed to a maximum shear force of 50kN. You are required to

calculate:

(i)

Average shear stress,

(ii)

Maximum shear stress,

(iii)

Shear stress at 25 mm above the neutral axis

Answer 1

In engineering, beams are of several types: Simply supported – a beam supported on the ends which are free to rotate and have no moment resistance. Fixed or Encastre – a beam supported on both ends and restrained from rotation. Over hanging – a simple beam extending beyond its support on one end.

Assumptions made in the theory of Pure Bending

The material of the beam is homogeneous¹and isotropic². The value of Young's Modulus of Elasticity is same in tension and compression. The transverse sections which were plane before bending, remain plane after bending also.

Similar to average normal stress (σ = P/A), the average shear stress is defined as the the shear load divided by the area. Oh In actual shear stress distribution, it is not uniform and the maximum shear stress will be higher than the average shear stress.

The maximum shear stress is equal to one half the difference of the principal stresses. It should be noted that the equation for principal planes, 2θp, yields two angles between 0° and 360°.