Question

(a) What is meant by the terms strength and toughness? Describe the difference between yield strength and ultimate tensile strength, highlighting how they might be determined [6 marks] (b) If a torque of loo kNm is applied to a solid circular shaft of 150mm diameter, what is the maximum shearing stress generated within in material? (e) Where is this stress located with respect to the shaft?

Answer 1

b) When a shaft is under the action of a torque, a shearing stress gets developed in the shaft, which varies from zero in the axis to a maximum at the outside surface of the shaft.

The shear stress in a solid circular shaft at a distance r from the axis can be expressed as:

St= T r / J   

where

St = shear stress

T = torque(

r = distance from center to stressed surface in the given position

J = Polar Moment of Inertia of an Area

therefore the maximum stress will be produced at the outersurface of the cylinder: i.e.: r = d/2.

==> St (max) = T* (d/2)/J ; J for solid circular shaft = pi * d^4 /32

==> St(max) = T*(d/2)/ (pi * d^4 /32) = T/ (pi * d^3 /16) = 16*T/ (pi * d^3 ) = 1.51 x 10^8 Pa.

c) the maximum stress will be produced at the outersurface of the cylinder

a) strength: Strength refers to resistance to deformation, and also to a large elastic range. A measure of the stress that a crack-free metal can bear before deforming or breaking under a single applied load.

toughness: Toughness is the resistance to failure or crack propagation. A measure of the amount of energy required to fracture a material that contains a crack.

yield strength and tensile strength difference:

Tensile strength measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks.

Specifically, the tensile strength of a material is the maximum amount of tensile stress that it can be subjected to before failure.

There are three typical definitions of tensile strength:

Yield strength - The stress a material can withstand without permanent deformation. For materials without a clear distinct yield point, yield strength is usually stated as the stress at which a permanent deformation of 0.2% of the original dimension will result, known as the 0.2% yield stress".
Ultimate strength - The maximum stress a material can withstand.
Breaking strength - The stress coordinate on the stress-strain curve at the point of rupture



Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the deformation will be permanent and non-reversible.
In structural engineering, yield is the permanent plastic deformation of a structural member under stress. This is a soft failure mode which does not normally cause catastrophic failure unless it accelerates buckling.