Structures I: Midterm A

Beams

Structural element characterized by horizontal members, resistance to bending and shear, and typically found in floor and roof systems.

Columns

Structural element characterized by vertical members, resistance to compression, typically found between floor and roof systems, and is sensitive to buckling.

Trusses

Structural element characterized by triangulated systems, works in tension and
compression, and typically found in roofs and bridges.

Cables

Structural element characterized by its resistance only to tension and is used in bridges, wheels, and
catenary structures.

Arches

Structural element used in compression only systems.

Load path

The route a load follows through a structure to the ground

Types of loads

compression, tension, bending, shear, torsion

tension

pulling force, seen in cables/suspension bridges/tensile membranes, and stretching/getting longer

compression

pushing force, seen in columns/arches/masonry, getting shorter

bending

combination of compression and tension, shape or force into a curve, for example breaking a pencil

shear

sliding force across planes in material, seen in slabs/short beams, sliding a book

torsion

twisting about a longitudinal axis, twist a towel/wrench, typically don’t want to design with this

Structural Systems

Load bearing walls, frame systems, shells and domes, and tensile systems

stone

high compressive strength and low tensile strength

wood

strong in tension and bending

brick

good in compression

steel

high strength to weight ratio, good in tension and compression

concrete

good in compression but bad in tension

composite

engineered wood, carbon fiber

units of mass

kg, lbf-s²/in, and slug

units of length

m, in, ft

units of force

N and lbf

units of stress or pressure

Pa, psi, and psf

types of forces

pull, weight, friction, and normal force

newtons law of inertia (1st law)

an object will remain at rest or in uniform motion in a straight line unless
acted upon by an external force.

Newtons second law of motion (law of acceleration)

F=ma

Newtons third law of motion

For every action, there is an equal and opposite reaction. sum of the forces = 0

Static Equilibrium

Moment equation

M=F×d⟂

M in moment equation

the moment of an axis

F in moment equation

A force

d⟂ in moment equation

the perpendicular distance between the force’s line of action and the axis of rotation

Positive moment direction

Negative moment direction

pin or hinge support

pin or hinge reaction

roller support

roller reaction

rocker support

rocker reaction

fixed support

fixed reaction

Simply supported

type of beam with a pin support on one end and a pin roller on the other

simply supported with an overhang

type of beam with a pin support in the middle, a roller on one end, and an overhang on the other end.

simply supported with two overhangs

type of beam with a pin and roller support in the middle and an overhang on each end.

cantilever beam

type of beam that is fixed on one end and free on the other

draw the free body diagram

find the ∑Fx=0

Ax=0k

find the ∑Fy=0

Ay=2k

find the ∑Ma=0

By=2k ↑

draw a free body diagram for the problem

Find the ∑Fx=0 reminder w=F/d

Ax=0k

Find the ∑Fy=0

Ay=30k

Find the ∑Ma=0

By=30k

Draw a free body diagram

Find the ∑Fx=0

Ax=0k

Find the ∑Fy=0

Ay=10k ↓

Find the ∑Ma=0

By=10k

draw a free body diagram

Find the ∑Fx=0

Ax=2k

Find the ∑Fy=0

Ay=3.46k

Find the ∑Ma=0

Ma=41.6kft

Draw the free body diagram

Draw the shear diagram

draw the Moment Diagram

In a moment diagram, a positive moment would go in what direction?

down

slope up on a shear diagram translates to what kind of curve in a moment diagram?

concave up

slope down on a shear diagram translates to what kind of curve in a moment diagram?

concave down

What kind of load does a cable carry?

tension

A moment is the 1 of a 2 and its 3 from its line of action to a given point.

1. product

2. force

3. distance

if an object is at rest the sum of the forces on an object…?

is equal to zero

beams and columns can take axial shear and moment

true

pinned supports can take two translational reactions

true

roller supports can take two translational reactions

false; roller supports can take one translational reactions

fixed supports can take two translational and one rotational reaction

true