STRENGTH OF MATERIALS

Flanged Bolt Coupling

consists of flanges rigidly attached to the ends of the shaft and bolted together. The torque is transmitted by the shearing force P created in the bolts.

breaking strength

rupture strength

Working stress

the actual stress of a material under a given loading.

Elastic limit

the limit beyond which the material will no longer go back to its original shape when the load is removed.

Allowable stress

the maximum safe stress that a material can carry.

Elastic limit

the maximum stress that may be developed such that there is no permanent or residual deformation when the load is entirely removed.

Yield point

the point at which material will have an appreciable elongation or yielding without any increase in load

Strain

the ratio of the change in length caused by the applied force, to the original length.

Poisson's Ratio

the ratio of the sidewise/lateral deformation (or strain) to the longitudinal deformation (or strain).

plastic range

the region from proportional limit P to rupture strength R

elastic range

the region in stress-strain diagram from origin O to proportional limit P.

Modulus of Resilience

the work done on a unit volume of material as the force is gradually increased from origin O to proportional limit P, in N-m/m^3. This may be calculated as the area under the stress-strain curve from the origin O to up to the elastic limit E.

tensile strength

ultimate strength

Bending stress

varies directly with the bending moment

Shearing stress

varies directly with the shear

Punching shear

A circular slug is about to be punched out of a plate, the resisting area is similar to the milled edge of a coin.

Thin walled pressure vessels

A cylindrical tank carrying a gas or fluid under a pressure is subjected to tensile forces, which resist bursting, developed across longitudinal and transverse sections.

Residual stress Structural stress Pressure stress Flow stress Thermal stress Fatigue stress

Categories of Stress

Strength of Materials

Deals with the nature and effects of stresses in the parts of engineering structures.

Bearing stress

Differs from compressive stress, as it is an internal stress caused by compression.

Shearing stress

Differs to tensile and compressive stresses, which are caused by forces perpendicular to the area on which they act.

Uniformly distributed load Uniformly varying or triangular load

Distributed load

Fatigue stress

Due to cyclic application of a stress; could be due to vibration or thermal cycling.

Residual stress

Due to the manufacturing processes that leave stresses in a material.

Single shear Double shear Punching shear

Examples of Shear

Thermal stress

Exists whenever temperature gradients are present in a material.

Shearing stress

Force parallel to the area resisting the force cause ______.

proportional limit

From the origin O to the point called ____, the stress-strain curve is a straight line.

Biaxial deformation

If an element is subjected simultaneously by tensile stresses, o_x and o_y, in the x and y directions. the strain in the x direction is o_x/E and the strain in the y direction is o_y/E.

Triaxial deformation

If an element is subjected simultaneously by three mutually perpendicular normal stresses o_x, o_y, and o_z, which are accompanied by strains E_x, E_y and E_z, respectively.

Torsion

In solid mechanics, it is the twisting of an object due to an applied torque. In circular sections, the resultant shearing stress is perpendicular to the radius.

Strength of Materials

Its principal object is to determine the proper size and form of pieces which have to bear given loads, or, conversely, to determine the loads which can be safely applied to pieces whose dimensions and arrangement are already given.

Flow stress

Occur when a mass of flowing fluid induces a dynamic pressure on a conduit wall

Structural stress

Produced in structural members because of the weights they support.

Tangential stress

Shearing stress is also known as ______.

Yield strength

Stress at which material exceeds the elastic limit and will not return to its original shape or length if the stress is removed.

Pressure stress

Stresses induced in vessels containing pressurized materials.

Circumferential stress

Tangential stress

positive, negative

Tensile deformation is considered ______ and compressive deformation is considered _______.

Double shear

The bolt resists the shears across two cross-sectional area.

Bearing stress

The contact pressure between the separate bodies.

Ultimate strength

The maximum ordinate in the stress-strain diagram is the ______ or tensile strength.

Stress

The mutual action between two bodies, or between two parts of a body, whereby each of the two exerts a force upon the other.

Stress

The ratio of the applied load to the cross-sectional area of an element in tension.

Factor of Safety

The ratio of ultimate strength to allowable strength.

Modulus of Resilience

The resilience of the material is its ability to absorb energy without creating a permanent distortion.

Single shear

The rivet resists shear across its cross-sectional area.

Rupture strength

The strength of the material at rupture.

Catenary

The theoretical shape of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight) and in equilibrium. The curve has a U shape, that is similar in appearance to the parabola, though it is a different curve.

Modulus of Toughness

The toughness of a material is its ability to absorb energy without causing it to break.

Tangential stress Longitudinal stress Spherical shell

Thin Walled Pressure Vessels

Bending stress Shearing stress

Two kinds of stress that act over a transverse section of a beam

Concentrated load Distributed load

Types of beam loading

Normal/Axial stress Shearing stress Bearing stress Thin-walled stress

Types of simple stress

Hooke's Law

Within the proportional limit, the stress is directly proportional to strain.

69 GPa

Young's Modulus of Aluminum

120 GPa

Young's Modulus of Copper

200 GPa

Young's Modulus of Steel

Flanged Bolt Coupling

a commonly used connection between two shafts.

Young's Modulus

a measure of the amount of force needed to produce a unit deformation.

Strain

a measure of the deformation of the material that is dimensionless.

Distributed load

acts over a considerable length of the beam.

Concentrated load

acts over a small part of the beam that can be assumed to act at a point.

Modulus of Toughness

the work done on a unit volume of material as the force is gradually increased from origin O to rupture strength R, in N-m/m^3. This may be calculated as the area under the entire stress-strain curve (from O to R).