Formulas

Question 1

What are the coefficients of thermal expansion and contraction for typical materials ?

Answer 1

Aluminum 0.0000128
Steel 0.0000065
Concrete 0.0000055
Glass 0.0000044
Wood 0.0000033

Question 2

Slenderness ratio of a wood column

Answer 2

SR=kL/b

SR= end condition x length in inches / cross section width of rectangle

Question 3

Moment for uniform load

Answer 3

M=wL^2/8

Moment =uniform load (w) x Length /8

Question 4

Shortening or elongation due to thermal change

Answer 4

Δ = e L Δt

Thermal change = coefficient of thermal expansion x original length x temperature

Question 5

Force

Answer 5

F=M(a)

Question 6

Moment about a point

Answer 6

M=Pd

Moment = Force x distance

Question 7

Equilibrium / stress

Answer 7

f=P/A

Question 8

Gallon of water

Answer 8

62.4 lbs / ft^3

Question 9

Slenderness ratio of a steel column

Answer 9

SR=kL/r
Slenderness Ratio= end condition (k) x unbraced length in inches /radius gyration
r = √ I /A

Radius of gyration = sqrt(moment of inertia (I)/Area

Question 10

Deflection equations: shortening of a column or elongation of a horizontal member

Answer 10

e=PL/AE

Deflection= force (P) x length / Area of cross section (A) x modulus of elasticity (E)

Question 11

Section modulus

Answer 11

S=bd^2/6
Section modulus = base x diameter(squared)/6
S= M/Fb
Section modulus = Moment/ bending stress
S=I/c
Section modulus = moment of inertia/ given constant

Question 12

Horizontal force on a retaining wall

Answer 12

F = w h^2/2

[Force exerted on the Retaining Wall= (fluid pressure provided) X (height)/2]

Question 13

Thermal strength in a restrained member

Answer 13

ft = E e Δt

Thermal stress = modulus of elasticity (E) x coefficient of thermal linear expansion (e) x temperature change

Question 14

Deflection of a beam

Answer 14

Delta=5wL^4(12^3)/384EI

Deflection = 5 x weight in lbs x length in feet x 12^4 /384 x 12 x modulus of elasticity x moment of inertia

Question 15

Retaining walls must support how much hydrostatic pressure

Answer 15

30 pounds per cubic foot

safety factor of 1.5

Question 16

Moment of Inertia

Answer 16

I=bd^3/12

Moment of inertia =base x depth /12

Question 17

Shear Force

Answer 17

R = V = wL /2

[Shear Resisting Force= (uniform load per ft) X (distance)]/2

Question 18

Point/Concentrated Load at the center of a member

Answer 18

M=P*L/4

[Moment = Point Load X length]/4

Question 19

Strain

Answer 19

ε = Δ/L

Deflection//original Length

Question 20

Modulus of Elasticity

Answer 20

E = f/ε

Modulus of Elasticity= Stress/Strain

Question 21

Factor of Safety

Answer 21

FS =RM/MOT

Resisting Moment/Overturning Moment

Or

FS= SM/OTM
Stabilizing Moment/Overturning Moment

Question 22

Dead Load Resisting Moment

Answer 22

Rm=1.5*Mot