Equations and Definitions

Question 1

Define Moment of Inertia and provide its equation

Answer 1

measure of an objects resistance to changes to its rotation

moment of inertia = base x depth ^3 / 12

rectangle moment of inertia = base x depth ^3 / 3

Moment of Inertia at Base = moment of inertia + area x distance from centroid to base ^2

Question 2

Define Deflection and provide its equation

Answer 2

The displacement of a structural element under a load

in a column:
deflection = force x length / area of cross section x modulus of elasticity

in a beam:
deflection = 5x weight (in pounds) x length ( in feet) x 12” ^4 / x 12” modulus of elasticity x moment of inertia

Question 3

Define Strain and provide its equation

Answer 3

The deformation of a material caused by external loads. Tensile loads stretch, and compressive loads shorten.

strain = deflection / original length

Question 4

Define Section Modulus and provide its equation

Answer 4

Is the ratio of a cross section’s second moment of area to the distance of the extreme compressive fibre from the neutral axis

section modulus = base x diameter ^2 / 6
section modulus= moment / bending stress
section modulus = moment of inertia / given constant

for a roof beam:
section modulus = moment / 1.25 x bending stress

Question 5

Define Modulus of Elasticity and provide its equation

Answer 5

A materials resistance to non permanent (or elastic) deformation (resistance / load deformation)

modulus of elasticity = stress / strain

Question 6

Define Factor of Safety

Answer 6

ratio of the ultimate strength of material to its working stress

Question 7

Define Shear

Answer 7

A strain produce by pressure in the structure when its layers are laterally shifted in relation to each other

Question 8

Define Moment and provide its equation

Answer 8

The tendency of a force to cause rotation about a given point of axis

to find equilibrium by taking moments about a point:
moment = force x distance

to fine the eccentric load (save as finding equilibrium)
moment = force x distance

To find Uniform Load:
moment = uniform load x length ^2 / 8

To fine point/concentrated load at the center of a member:
moment= point load x length / 4

Question 9

Define stress

Answer 9

the resistance of a body to a load (called an internal force) and measured in kips

Question 10

Flexural stress

Answer 10

the act of flexing or the state of being flexed (bending)