Equation to memorize

Question 1

Slenderness ratio

Answer 1

Slenderness Ratio (SR) = end condition (k) x unbraced length in inches (L) /
 radius of gyration (r)"

Question 2

radius of gyration

Answer 2

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

Question 3

To find shortening of a column or elongation of a horizontal member

(deflection)

Answer 3

Deflection (e) = Force (P) x Length (L) / Area of cross section (A) x Modulus of elasticity (E)”

Question 4

To find deflection of a beam

(deflection)

Answer 4

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)”

Question 5

To find shortening or elongation due to temperature change

Answer 5

Thermal Change (∆) = Coefficient of Thermal Linear Expansion (e) x original length (L) x temperature change (∆t)”

Units are inches

Question 6

To find thermal strength in a restrained member

Answer 6

Thermal Stress (ft) = Modulus of Elasticity (E) x Coefficient of Thermal Linear Expansion (e) x temperature change (∆t)”

Units are inches

Question 7

To find slenderness ratio of a wood column (should be less than or equal to 50)

Answer 7

Slenderness Ratio (SR) = end condition (k) x unbraced length in inches (L) / cross section width of rectangle (b)”

Question 8

To find the horizontal force on a retaining wall

Answer 8

Force(P)=total load(W)xheightofwall(h)2 /2

Question 9

To find equilibrium by taking moments about a point:

Answer 9

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

Question 10

To find base shear (units = kips)

Answer 10

Base Shear (V) = Seismic response coefficient (Cs) x effective seismic weight of “ building(W)

Question 11

To find seismic designcoefficient

Answer 11

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)

Question 12

To find force {units = kips or lbs}

Answer 12

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

Question 13

Section modulus

{units = inch3}

Answer 13

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

Question 14

Earth Pressure on a wall

Answer 14

(P) = 30 lb/ft3 x height of wall

Question 15

to find wind pressure

Answer 15

p=wind pressure

K=a constant

V=wind velocity

Question 16

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

{units = inch4}

Answer 16

MomentofInertia(I)=Base(b)xdepth(d)3 /12

Question 17

To find stress

Stress (f): the resistance of a body to a load (also called an internal force) and
measured in kips (K)

Answer 17

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

Question 18

To find area of a circle

Answer 18

A= area

π=3.14

r=radius of circle

Question 19

To find uniform load; moment

{units = kip ft, lb ft, kip in, or lb in}

Answer 19

Moment(M)=uniformload(w)xlength(L)2 /8”

Question 20

The 3 Section Modulus Equations

Answer 20

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)

Question 21

To find total load

Answer 21

W= total load

w=weight

L=length

Question 22

To find defelction given total load (W)

Answer 22

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)”

Question 23

What is the seismic formula and the variables that it includes

Answer 23

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.

Question 24

To find Strain

Answer 24

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

Question 25

To find modulus of elasticity

Answer 25

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