Equations Flashcards
f = P/A
Stress (f) = Total Force (P) / Area (A)
F = Ma
Force (F) = Mass (M) x Acceleration (a)
F = w^2h / 2
To find the horizontal force on a retaining wall
Force (F) = soil pressure (w) x height of wall (h)2 / 2
M = Pd
Moment (M) = Force (P) x distance (d)
Moment (M) = uniform load derived point load (W) x length (L) / 8
M = WL/ 8
M = PL / 4
Moment (M) = Point Load (P) x length (L) / 4
S = bd^2 / 6
Section Modulus (S) = Base (b) x diameter (d)^2 / 6
S = M / Fb
Section Modulus (S) = Moment (M) / Bending Stress (Fb
S = I / c
Section Modulus (S) = Moment of Inertia / given constant (c)
I = bd^3 / 12
To find Moment of Inertia (occurs about the centroidal axis)
Moment of Inertia (I) = Base (b) x depth (d)3 /12
I = bd^3 / 3
Rectangle Moment of Inertia
fb = M / S
Bending Stress (fb) = Moment (M) / Section Modulus (S)
Fa = P / A
To find axial stress (max axial stress occurs along entire cross section)
Axial Tension or Compression Stress (fa) = Axial Tension (P) / Area (A)
E = f / ε
Modulus of Elasticity (E) = Stress (f) / Strain (ε)
ε = e / L
Strain (ε) = Deflection (e) / Original Length (L)
e = PL / AE
To find shortening of a column or elongation of a horizontal member:
Deflection (e) = Force (P) x Length (L) / Area of cross section (A) x Modulus of
elasticity (E)
∆ = 5wL4 / 384EI
To find deflection of a beam
Deflection (∆) = 5 x weight in lbs (w) x length in feet x 12”^4 (L^4) / 384 x 12”
modulus of Elasticity (E) x Moment of Inertia (I)
∆ = eL∆t
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)
ft = Ee∆t
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)
SR = kL / r
To find slenderness ratio of a steel column (should be less than or equal to 200):
Slenderness Ratio (SR) = end condition (k) x unbraced length in inches (L) /
radius of gyration (r)
r = √I / A
Radius of gyration (r) = √moment of inertia (I) / Area
SR = kL / b
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)
S=bd^2/6
Section Modulus= base x depth squared/6 (section modulus for rectangle)
S=I/C
Section Modulus=moment of inertia/distance from end to center
Density of Water
62.4 pcf
Density of Concrete
150 pcf
Wind Speed to Wind Pressure
0.00256 V^2
