EGB121 - Engineering mechanics

Average normal stress

P/A

Average normal strain

Change in length divided by original length

Strain hardening

Between elastic limit and ultimate tensile strengh

Necking

Between ultimate tensile stress and fracture point

Young's modulus

Stress/Strain

Couple moment

Same magnitude but opposing directions (only effect is producing rotation)

Two force member

An element with pins and both ends and no loads in between (doesn't need to be written as two reactions)

Hinges/pins in the beam

Use the frames/machines method instead of beam methods

Journal bearing

Prevents translation in x and z

Thrust bearing

Prevents translation in x and y and z

x bar

Centroid

Find the centroid of a non-standard shape

integral xtilda dA divided by integral of dA (xtilda = centroid of integrating element)

Centroid of a composite body

sum of xiAi/totalA

Moment of inertia (x)

Integral of x^2 dA

Parallel axis theorem (x)

Sum of Ix' + Area*d^2

Saint-Venant's principle

The stress distribution will even out and become uniform over the section from a point load at a distance equal to the largest dimension of the cross-section

Principle of superposition

Resultant stress or displacement at a given point can be determined by algebraically summing the stress or displacement due to each individual force

Statically indeterminate

Not enough equations of equilibrium to solve for the unknowns

Compatibility condition

If a member is statically indeterminate but something else like two fixed points prevent displacement in a certain way

Modulus of resilience

Area under elastic part of stress-strain curve

Modulus of toughness

Area under whole stress-strain curve

Greater ductility

Longer plastic region

Higher toughness

Greater area under curve

UDL shear force diagram

A straight line with a slope equal to the load density

Maximum bending moments occur at what point of shear

0 shear

Simply supported beams bending moment at each end

0

Cantilever bending moment diagram

0 bending at the free end and maximum at the fixed end

Positive shear force

Causes clockwise rotation - down on left, up on right

Positive bending moment

Causes compression at the top of the beam - upwards and outwards from centre

Axial loading compression and tension

Must check whether a section is in tension or compression (positive vs negative is not always the case)

Negative displacement

A section/member is in compression

Positive displacement

A section/member is in tension

A clockwise external bending moment causes

A positive jump in the bending moment diagram

Slope of the shear force diagram

Intensity of the bending moment

Power =

Torque times omega

Positive torque

Clockwise

Torque

Same as to calculate moments (clockwise torque is positive)

1/rho =

M/EI