[Physics Class Notes] on Shearing Stress Pdf for Exam

What is Shearing Stress?

You may have tried to break a thick wooden stick, but failed in the attempt to do so. You may have tried to break it by stepping on it really hard. Here, what made it break is its shear stress.

Shear stress is the deforming force acting per unit area and in the direction perpendicular to the axle of the member. The impact of your load when you step in a wooden stick causes two types of stresses, these are:

• Bending Stress, which is parallel to the axle of the member also called flexural stress.

• Shear Stress, which acts in a direction perpendicular to the axle of the member.

[]

Do you know?

Shear means ‘to cut off’. When force is applied over the surface area of a rigid body (force acting in a direction parallel to the surface) then this force tries to cut off one part of the body from the other. As a result of this the body gets deformed and hence strain is produced (shear strain- the angular deflection of the body from its original position). Due to the rigidity of the body, it resists the deformation caused and a restoring force (equal and opposite to the applied force) is developed along the surface of the body as per Newton’s 3rd law of motion). This restoring force of the body tends to oppose the shearing effect of the applied force. Thus shear stress is just an effect of shear strain.

Shear Force Definition

It is a force that acts on a plane which passes through the body. The shear forces are unaligned and separate the structure into two different parts in opposite directions. The shear force acts in a perpendicular direction to the larger part of the body.

Shear force, in a beam, acts perpendicular to the longitudinal (x) axis. The beam’s ability to resist shear force is much more important as compared to its ability to resist axial force. Axial force acts parallel to the longitudinal axis of the beam.

The given below figure represents a simple-supported beam of length L under a uniform load q:

[]

This beam has the following support reactions:

[]

Where,

● Rl = is the reaction at the left end of the beam

● Rr = is the reaction at the right end of the beam.

The shear forces at the end points of the beam are equivalent to the vertical forces of the support reactions. The shear force F(x) at any other point x, apart from the end points on the beam is calculated by using the shear force formula. This formula is:

F(x) = Rl – qx = qL/2 – qx = q(L/2 – x)

Where,

x = distance of the point from the left end of the beam.

Q = first moment of area in m^3

The shear stress acts in a direction parallel to that of the surface. Shear stress causes one object to slip over the other. It deforms the original shape of the object, like converting a rectangular shaped object into a parallelogram. It is the ratio of the applied force (F) to the cross-sectional area (A) of the structure/beam. Shear stress acts in a direction which is perpendicular to the normal stress. The shear stress is denoted by ‘Ԏ’.

Shear Stress Formula: Ԏ = F/A

[]

Where,

F = force acting on the structure,

A = area of cross-section of the body.

Beams are also acted upon by transverse forces, which accounts for both bending moment M(x) and shear forces V(x)

Expression of distribution of shear stress in a body

Ԏxy = VQ/It

Where,

V = shear force in the cross section,

Q = First moment of area

I = moment of inertia of the area,

t = width of the section.

Shear Stress Units

The units of shear stress are similar to that of any other type of stress. The unit for shear stress is N/m^2 or Pa (Pascal) in the SI system and lbf/ft^2 in the English system.