3 fundamental principles of equilibrium apply to all buildings:
- The sum of all vertical forces acting on a body must be equal to zero
- The sum of all horizontal forces acting on a body must be equal to zero
- The sum of all moments acting on a body must be equal to zero
What is the difference between loads and stresses?
Loads = external forces resulting from the weights of such things as people, snow, wind, building materials
Stresses = the internal resistance to loads
What are 5 types of forces on a building?
- Collinear forces = those whose vectors lie along the same straight line
- Concurrent forces = those whose lines of action meet at a common point
- Nonconcurrent forces = have lines of action that do not pass through a common point
- Parallel noncurrent forces = lines of action that are parallel but do not pass through a common point (ie forces acting on a beam)
- Coplanar forces = those whose lines of action all lie within the same plane
**Structural forces in a building may be a combination of these types **
3 basic types of stresses:
- Tension = stress in which the particles of the member tend to pull apart under load
- Compression = particles of the members are pushed together and members tend to shorten
(Bending = type of tension and compression) - Shear = stress in which particles of a member slide past each other
(Torsion = type of shear in which a member is twisted)
What is the general equation for stress?
f = P/A
stress (f) equals total force applied (P) over the area (a)
What is thermal stress?
stresses that occur when a material expands/contracts when subjected to a change in temperature
What is the equation for thermal stress on an unrestrained material?
What is the equation for thermal stress on a material restrained at both ends?
unrestrained thermal stress = alpha x L x (delta T)
where alpha = coefficient of linear expansion
restrained thermal stress = E x (alpha) x (deltaT)
where
E = modulus of elasticity
alpha = coefficient of linear expansion
What is strain? What is the equation for strain?
Strain = deformation of a material caused by external forces.
strain = e / L
where e = total deformation
L = length
Hooke’s Law:
As force is applied to a material, the deformation (strain) is directly proportional to the stress, up to a certain point. After a certain point (elastic limit), the material will begin to change length at a faster ratio than the applied force.
What is the elastic limit?
At any stress up to the elastic limit, the material will return to its original size if the force is removed. At any stress above the elastic limit, there will be permanent deformation, even after the force is removed.
What is the yield point?
A point slightly above the elastic limit at which the material continues to deform with very little increase in load.
What is ultimate strength?
Ultimate strength = the point just before the material breaks completely
What is the modulus of elasticity?
A material’s stiffness. A measure of a material’s resistance to deformation. Every material has a characteristic ratio of stress to strain.
What is equation for the total strain (deformation) of a material under a given load?
e = (PL) / (EA) E = modulus of elasticity
6 properties of a section that affect how a section can efficiently resist a load:
- Area (f=P/A)
- Centroid center of gravity
- Statical moment
- Moment of inertia
- Section modulus
- Radius of gyration
What is statical moment?
equation?
units?
It helps find the centroid of unsymmetrical areas.
Statical moment = Area x (distance from one of the axis)
Note: the sum of the statical moment of the parts = the statical moment of the entire section.
Units = inch
What is the moment of inertia?
Moment of inertia = I = measure of the bending stiffness of a structural member’s cross-sectional shape
Equation for moment of inertia in…
- rectangular sections, about the centroidal axis parallel to the base =
- rectangular sections about the axis through the base =
- composite areas
I = (b*(d^3)) / 12
I = (b(d^3)) / 3
I = I_x + A(x^2)
where x = distance from centroid axis for the moment of inertia axis
What is the law of cosines?
c^2 = a^2 + b^2 - 2abcosC
where lower case = angles and upper case = lengths
What is the law of sines?
a/sinA = b/sinB = c/sinC
What is the most common yield strength of steel?
50 ksi
In concrete, if you post tension a member you can reduce the depth by about
30%
The required depth of a 2-way system is about ___ less than a one way system
20-30%
What are 3 characteristics of the flat plate 2 way structural system?
shallowest depth
simplest formwork
heaviest structure
