Mechanics of Materials Midterm #1

Positive sign conventions if you’re taking a left hand side…

N = out of face, V= down, M= counterclockwise- always ‘holding water’

For a distributed load… remember that it’s moment contribution to an internal moment diagram equation…

acts at the halfway point of the distributed load, and if the load starts at ‘a’ then (x-a) is the length of it, so M(x) = (x-a)* (x-a)/2 * height

Similar triangle equation

a/x = b/x+L if a and b are heights of a triangle and x and x+L are their respective lengths, can also be set equal to theta or tangent theta.

If normal stress ___ it is ____ whereas if it _____ it is ______

pulls, tensile stress (positive); pushes, compressive stress (negative)

Stress question

Force / Area

Double Shear Stress equation?

Force/ Area *2

Force in a pin equation

Factor of Safety

F _fail/ F _allow =

Newtons an mm² gives what units?

Mpa

Stress and Strain tensors must be?

Symmetrical accross the diagonals

Engineering Shear Strain?

pi/2 - theta

Law of Cos?

a²=b²+c²-2(b)c*cos(alpha)

Law of Sines

c/ sin(theta) = b/sin(beta)= a/sin(alpha)

Process of Small angle approximation?

where dY= radius* degree* pi/180 (this term converts the degrees into radians)

sin(alpha)= h/L

or Cos(alpha)= b/L

Hooke’s Law

shear= E* strain

Young’s Modulus?

E, the slope of the stress-strain graph in the elastic region

Deformation in the ‘yielding’ section of the graph is considered?

Plastic deformation

How do calculate plastic deformation?

Total strain= E plastic + (shear/ E)

where total strain can be obtained from the graph

Sections of the stress-strain diagram in order

Elastic Region, Yielding, Strain Hardening, Necking

the ____ and the ____ occur at the end of the elastic region very close to one another but ____ is first

Proportional Limit, Yield Point, Proportional Limit

Highest point on the graph?

Ultimate stress

Last point on the graph?

Fracture Stress

Ductile materials

Experience significant plastic deformation before fracture

Brittle material

experience little or no plastic deformation before fracture but the handle compressive loads well.

Displacement equation

D = N*L/ E*A

Displacement to Normal Stress equation