Equations

Question 1

f = P/A

Answer 1

Stress (f) = Total Force (P) / Area (A)

Question 2

F = Ma

Answer 2

Force (F) = Mass (M) x Acceleration (a)

Question 3

F = w^2h / 2

Answer 3

To find the horizontal force on a retaining wall

Force (F) = soil pressure (w) x height of wall (h)2 / 2

Question 4

M = Pd

Answer 4

Moment (M) = Force (P) x distance (d)

Question 5

Moment (M) = uniform load derived point load (W) x length (L) / 8

Answer 5

M = WL/ 8

Question 6

M = PL / 4

Answer 6

Moment (M) = Point Load (P) x length (L) / 4

Question 7

S = bd^2 / 6

Answer 7

Section Modulus (S) = Base (b) x diameter (d)^2 / 6

Question 8

S = M / Fb

Answer 8

Section Modulus (S) = Moment (M) / Bending Stress (Fb

Question 9

S = I / c

Answer 9

Section Modulus (S) = Moment of Inertia / given constant (c)

Question 10

I = bd^3 / 12

Answer 10

To find Moment of Inertia (occurs about the centroidal axis)

Moment of Inertia (I) = Base (b) x depth (d)3 /12

Question 11

I = bd^3 / 3

Answer 11

Rectangle Moment of Inertia

Question 12

fb = M / S

Answer 12

Bending Stress (fb) = Moment (M) / Section Modulus (S)

Question 13

Fa = P / A

Answer 13

To find axial stress (max axial stress occurs along entire cross section)
Axial Tension or Compression Stress (fa) = Axial Tension (P) / Area (A)

Question 14

E = f / ε

Answer 14

Modulus of Elasticity (E) = Stress (f) / Strain (ε)

Question 15

ε = e / L

Answer 15

Strain (ε) = Deflection (e) / Original Length (L)

Question 16

e = PL / AE

Answer 16

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)

Question 17

∆ = 5wL4 / 384EI

Answer 17

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)

Question 18

∆ = eL∆t

Answer 18

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)

Question 19

ft = Ee∆t

Answer 19

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)

Question 20

SR = kL / r

Answer 20

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)

Question 21

r = √I / A

Answer 21

Radius of gyration (r) = √moment of inertia (I) / Area

Question 22

SR = kL / b

Answer 22

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)

Question 23

S=bd^2/6

Answer 23

Section Modulus= base x depth squared/6 (section modulus for rectangle)

Question 24

S=I/C

Answer 24

Section Modulus=moment of inertia/distance from end to center

Question 25

Density of Water

Answer 25

62.4 pcf

Question 26

Density of Concrete

Answer 26

150 pcf

Question 27

Wind Speed to Wind Pressure

Answer 27

0.00256 V^2