CE4013 Definitions

The maximum stress a material can withstand

The stress above which plastic deformation occurs

The force per unit cross-sectional area

The fractional change in length under load

The force multiplied by the perpendicular distance between the line of action and the pivot

Two equal forces acting in the opposite direction. The resultant force is zero, however the applied moment is non-zero (unless the points are the same distance from the pivot)

The force multiplied by the distance between the lines of action of the forces

Provides restraint in the vertical and horizontal directions. It permits rotation.

Horizontal movement and rotation is permitted. Motion perpendicular to the rollers is restricted.

Vertical and horizontal movement and rotation are restricted.

A structure built out of members where elements are connected by frictionless joints. The structure is stable under loads applied at the joints.

m+r

2j-3

All members are idealised as straight lines. All joints are pins so moments aren't transmitted.

The region within which, when the stress is removed, the object will return to its original size and shape

The region within which, when the deforming force is removed, the object will not return to its original shape and size - permanent deformation will remain

The force is applied parallel to the face of the element. 3 other forces are required to maintain equilibrium, creating two balanced moments.

Distance of shear/original length=tan theta≈ theta where the angle is in radians and is small.

This is produced by applying equal tensile or compressive forces on all six faces.

There is no thermal stress unless expansion or contraction (∆L) is restricted

Change in length equals the original length multiplied by the coefficient of thermal expansion and the change in temperature.

The strain produced in a material is directly proportional to the stress producing it.

1/3E<G<½E

This is the elastic response of the material to equilateral tension or compression. p=K∆ where ∆ is volumetric strain.

V=lateral strain (x)/ axial strain (y)

Have mechanical properties/ elastic constants that are the same in all directions.

Have differing mechanical properties/ elastic constants depending on the direction of stressing.

Have different properties/ elastic constants in all 3 mutually perpendicular directions.

The point at which there's a sudden yield with little to no increase in stress/ load.

0.2% proof force/ original cross-sectional area

Force x displacement

To increase the strength of ductile materials. The yield plateau only happens once, the following time, there's a direct transition from elastic to plastic behaviour.

The dislocation line will move through the lattice (one atomic spacing) when a shear stress is applied. This means the crystal shape changes without loss of structure or mechanical fracturing. A visible amount of plastic slip is due to a large number of dislocations. Slip defects are unlikely to cross grain lines due to differing atomic orientations. When the slip defects reach the grain, strain hardening occurs.

Require less energy to fracture and have a short plastic deformation region

Require more energy to fracture and have a long plastic deformation region

The work done per unit volume to give a certain strain

The tendancy of materials to deform in response to stress over time. (Constant load or stress)

Repeated cyclic loading to a stress where maximum stress is less than the UTS

The beam is originally straight and unstressed. The material of the beam is homogenous (the same throughout) and isotropic. Young's Modulus (E) is the same in tension and compression. Plane cross-section remains plane before and after (no shear force - pure bending - is assumed). This is because the shear force doesn't affect stresses much as long as beam length far exceeds the cross-sectional area.

In the deformed element subjected to a bending moment, a surface with no change in length along the longitudinal axis is called the neutral surface.

Radius x Theta