Shear Force

force acting on a substance in a direction perpendicular to the extension of the substance. The sum of forces to the left or right of a point in question.

Bending moment

Internal moment causing beam to bend. Sum of the moments to the left or right of a point in question.

We care about these kinds of beam failures:

1. Shear failure 2. Bending failure 3. Excessive deflection

Beam deflection is caused by?

Load, span, and end fixity

Deflection

The distance a beam or structure deforms under loading, typically due to bending in a beam. Geometry and material.

support types

Fixed, Pin/Hinge, Roller Support, Cantilever/free end

centroids

the center of mass of a geometric object of uniform density.

Live Load

The weight of movable objects such as people, furnishings, machines, vehicles, and goods in or on a building. More unpredictable.

dead load

the weight of the structure itself

Stress

force/area

Strain

strain is the resulting deformation from an applied force

How do you increase/reduce the horizontal/vertical reactions of an arch or sagging cable?

Reduce the horizontal reactions by making the arch taller, or making the cable sag greater. Reduce the vertical reactions by decreasing the total weight or dead load across the span

truss identification

2j = #members + #reactions

strength

ability to carry a load

stiffness

The ability of an object to resist deformation

Ductile failure

The desirable failure mode. Gives warning and enough time for the occupants of the building to escape prior to collapse.

Brittle failure

Undesirable failure. Sudden and deadly, breaking/crumbling

elastic range

the range of unit stresses for which a material exhibits elastic deformation

plastic range

the range beyond the elastic limit extending to the point of rupture

yeild point