Cloned from: ARE-Structures

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a Force
A push or pull exerted on an object.Forces are drawn as arrows showing direction with the length indicating magnitude.
a Load
a force applied to a body.
a Stress
The resistance of the body to the load.
Line of Action
A line parallel to and in line with the force.
Concurrent Forces
When the lines of action of several forces pass through a common point.
Nonconcurrent Forces
When the lines of action of several forces do not pass through a common point.
The sum of two or more forces with the same line of action.
3 Things to get the resultant.
1.The order drawn makes no difference.
2.The resultant is directed away form the starting point.
3.The resultant is concurrent with the orginal forces.
A force equal in magnitude to the resultant, but opposite in direction with the same line of action
basic trig functions
Right Triangle ABC
sin θ=A/C cos θ=B/C tan θ=A/B. Thus A =C sin θ and B=C cos θ. Also C²=A²+B² from which C=√A²+B²
A Momenet
The tendency of a force to cause rotation about a given point or axis.
center of moments
axis of rotation
The point or axis of a moment.
moment arm
lever arm
the distance of a moment measured in a direction perpendicular to the line of action of the force.
Magnitude of the moment

Magnitude of the force (in kips or pounds) multiplied by its distance from the given point (in feet or inches) foot*pounds
a couple
Two forces equal in magnitude, but opposite in direction, and acting at some distance from each other.
Objects at rest.
The three conditions of equilibrium
  1. The summation of all the horizantal forces acting on the body must equal zero (ΣH=0)
  2. The summation of all the vertical forces acting on the body must equal zero (ΣV=0)
  3. The summation of all the moments acting on the body must equal zero (ΣM=0)
The centroid
Equivalent to the center of gravity of the area: all of the area may be considered concentrated at the centroid without affecting the moment of the area about any axis.
statical moment
The area multiplied by the perpendicular distance from the centroid of the area of the axis
The moment of inertia
The sum of the products obtained by multiplying all of the infinitesimal elements of area by the sqaure of their distances from the axis.
moment of inertia for a rectangle about it's centroidal axis
I = bd3/12
moment of inertia of a rectangle about its base
I = bd3/3
Total stress
the total internal force on a section and is measured in pounds or kips.
Unit stress
the stress per unit of area of the section and is measured in pounds per sqaure inch (psi) or kips per sqaure inch (ksi)
shear stress
two members tend to slide past each other
the deformation, or change in size, of a body caused by external loads.
total strain
the total elongation or shortening of a body, and is represented by Δ
Unit strain
the total strain divided by the original length.
Hooke's Law
Up to a certain stress, called elastic limit, unit stress (P/A) is directly proportional to unit strain (Δ/L).
The modulus of elasticity
Young's modolus
the unit stress divided by the unit strain for a given material. (the greater the E value the of a material, the more stress it takes to deform it)
yeild point
a point where a material continues to stretch with no increase in load.
ultimate strength
the maximum unit stress of a material before it fractures
working stress
allowable stress
the maximum units stress permissible in a structural member.
coefficient of thermal expansion
The ratio of unit strain to temperature change.
a beam
it is a member which resists loads perpendicular to itself and rests on supports.
s simple beam
rests on supports at each end, and whose ends are free to rotate.
cantilever beam
supported at one end only, and which is restrained against rotation at the end.
overhanging beam
rests on two or more supports and has one or both ends projecting beyond the support.
continuous beam
rests on more than two supports
fixed end beam
restrained (fixed) against rotation at its ends.
the forces acting at the supports which hold the beam in equilibrium
concentrated load
when a single (concentrated) load acts at one point on the beam.
uniform load
the load acts over the length of the beam.
statically determinate beams
beams for which the reactions can be found from the equations of equilibrium

ie simple, cantilever and overhanging beams
statically indeterminate beams
beams whose reactions cannot be found from the equations of equilibrium.

ie continuous and fixed end beams
Vertical shear (V)
at any section of a beam is the algebraic sum of the forces that are on one side of the beam.
bending moment (M)
algebraic sum of the moments about the section of the forces on one side of the section.
The two points of greatest interest on a shear diagram
1. where the shear passes through zero
2. the greatest maximum value
flexure formula

f = My/I or f = Mc/I or f = M/S (S=I/c the section modulus)
f=flexural (bending) unit stress in tension or compression, in psi
M=bending moment, in inch-lbs.
y=the distance from the neutral axis to the fiber under consideration, in inches
I=the moment of inertia of the beam cross-section about the neutral axis, in inches4
horizontal shear stress
v = VQ/Ib or 3V/2bd (rectangular cross sections)
Q=statical moment
I=moment of inertia
b=thickness of the beam at the plane under consideration.
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