DEFINITIONS

The proportionality limit is the value of stress on the stress-strain curve at which the curve first deviates from a straight line.

The elastic limit is the value of stress on the stress strain curve at which the material has deformed plastically; that is will no longer return to its original size and shape after removing the load.

The yield point is the value of stress on the stress- strain curve at which there is a significant increase in strain with little or no increase in stress.

The ultimate strength is the highest value of stress on the stress-strain curve.

The yield stress is the value of stress at the yield point or yield strength.

The yield strength is the value of stress on the stress- strain curve at which a straight line drawn from a strain value of 0.002 in/in or (m/m) and parallel to the straight portion of the stress- strain curve, intersects the curve.

The modulus of elasticity E, is a measure of the stiffness of a material determined by the slope of the straight- line portion of the stress-stress strain curve. It is the ratio if the change of stress to the corresponding change in strain.

The percentage elongation is the ration of the plastic elongation of a tensile specimen after ultimate failure within a set of gage marks to the original length between the gage marks. It is one measure of ductility.

A ductile material is one that can be stretched, formed, or drawn to a significant degree before fracture. A metal that exhibits a percentage elongation greater that 5.0% is considered to be ductile.

A brittle material is one that fails suddenly under load with little or no plastic deformation. A metal that exhibits a percentage elongation less than 5.0% is considered to be brittle.

The design stress is that level of stress which may be developed in a material while ensuring that the loaded member is safe.

To compute design stress, two factors must be specified: the design factor N and the property of the material on which the design will be based. Usually for metals the design stress is based on either the yield strength sy or the ultimate strength su of the material.

The design factor N is a number by which the reported strength of a material is divided to obtain the design stress d .

The following equation can be used to compute the design stress for a certain value of N:

d = sy / N based on yield strength

d = su / N based on ultimate strength

the ration of the shearing stress to the shearing strain is called the modulus of elasticity in shear or the modulus of rigidity, and is denoted by G.

that is

G = shearing stress =

shearing strain

Poisson’s ration: the ration of lateral strain on the element to the axial strain is called Poisson’s ratio and is a property of the material from which the load carrying member is made

Shearing forces are internal forces developed in the material of a beam to balance externally applied forces in order to ensure equilibrium in all parts of the beam.

Bending moments in addition to shearing forces, are developed in beams as a result of application of loads acting perpendicular to the beam.