Equation to memorize Flashcards
Slenderness ratio
Slenderness Ratio (SR) = end condition (k) x unbraced length in inches (L) / radius of gyration (r)"
radius of gyration
Radius of gyration (r) = √moment of inertia (I) / Area
To find shortening of a column or elongation of a horizontal member
(deflection)
Deflection (e) = Force (P) x Length (L) / Area of cross section (A) x Modulus of elasticity (E)”
To find deflection of a beam
(deflection)
Deflection (∆) = 5 x weight in lbs (w) x length in feet x 12”4 (L4) / 384 x 12” modulus of Elasticity (E) x Moment of Inertia (I)”
To find shortening or elongation due to temperature change
Thermal Change (∆) = Coefficient of Thermal Linear Expansion (e) x original length (L) x temperature change (∆t)”
Units are inches
To find thermal strength in a restrained member
Thermal Stress (ft) = Modulus of Elasticity (E) x Coefficient of Thermal Linear Expansion (e) x temperature change (∆t)”
Units are inches
To find slenderness ratio of a wood column (should be less than or equal to 50)
Slenderness Ratio (SR) = end condition (k) x unbraced length in inches (L) / cross section width of rectangle (b)”
To find the horizontal force on a retaining wall
Force(P)=total load(W)xheightofwall(h)2 /2
To find equilibrium by taking moments about a point:
Moment (M) = Force (P) x distance (d)”
To find base shear (units = kips)
Base Shear (V) = Seismic response coefficient (Cs) x effective seismic weight of “ building(W)
To find seismic designcoefficient
I(importance factor)
R(response modification coefficient)
Sds (attenuation parameter that varies according to soil condition and the structures fundamental period)
T (Actual period of building)
Cs(seismic design coefficeint)
To find force {units = kips or lbs}
Force (F) = Mass (M) x Acceleration (a)
Section modulus
{units = inch3}
Section Modulus (S) = Moment of Inertia / given constant (c)
Earth Pressure on a wall
(P) = 30 lb/ft3 x height of wall
to find wind pressure
p=wind pressure
K=a constant
V=wind velocity
To find Moment of Inertia (occurs about the centroidal axis)
{units = inch4}
MomentofInertia(I)=Base(b)xdepth(d)3 /12
To find stress
Stress (f): the resistance of a body to a load (also called an internal force) and
measured in kips (K)
Stress (f) = Total Force (P) / Area (A)
To find area of a circle
A= area
π=3.14
r=radius of circle
To find uniform load; moment
{units = kip ft, lb ft, kip in, or lb in}
Moment(M)=uniformload(w)xlength(L)2 /8”
The 3 Section Modulus Equations
SectionModulus(S)
Base(b)
diameter(d)
Moment (M)
Bending Stress (Fb)
Moment of Inertia (I)
given constant distance from the cross section’s neutral axis to its extreme fibers (c)
To find total load
W= total load
w=weight
L=length
To find defelction given total load (W)
Deflection (∆) = 5 x Total Load (W) x length in feet x 12”4 (L3) / 384 x 12” modulus of Elasticity (E) x Moment of Inertia (I)”
What is the seismic formula and the variables that it includes
S(DS) and S(D1) are the design acceleration, which depend on location of building site
I is the importance factor, accounting for the occupancy of the building
R is the the response modification factor, related to the type of structural system employed
T is the fundamental period of vibration of the building and is a function of building height.
To find Strain
Strain (ε) = Deflection (e) / Original Length (L)
To find modulus of elasticity
Modulus of Elasticity (E) = Stress (f) / Strain (ε)
