formulas

Question 1

strain =

Answer 1

change in length / original ength

Question 2

stress =

Answer 2

force (perp.) / cross sectional area

Question 3

moment of inertia for a rectangular section

Answer 3

bd^3/12

Question 4

second moment of area

Answer 4

sum of moments of inertia (for sections) + sum of Ah^2 (for sections)
- h = distance from middle of section to (neutral) axis

Question 5

poisson’s ratio

Answer 5

lateral strain/ axial or longitudinal strain

Question 6

the neutral axes/ the centroid values

Answer 6

sum of Ay or Ax / sum of areas
- where y and x are the distance from the “reference axis”

Question 7

elastic or young’s modulus

Answer 7

stress/ strain

Question 8

condition for determinate structure (supported beams)

Answer 8

no. of reactions is greater than or equal to the no. of equilibrium equations (3 or 4 if internal pin)

Question 9

condition for determinate strucuture (trusses)

Answer 9

m + r = 2j
- m= members, r = reactions, j = nodes or joints

Question 10

degree of redundancy

Answer 10

R - E
- R= reactions, E= no. of equilibrium equations

Question 11

UDL

Answer 11

W = ωL
- ω= unit load, L=length of beam

Question 12

Partially distributed load

Answer 12

W = ω(x2-x1)
- ω= unit load, x2-x1= length of PDL

Question 13

varying distributed load (including where it acts)

Answer 13

W = 1/2* ω* (x2-x1)
- ω= unit load, x2-x1= length of PDL

acting as a point load a 1/3 of the distance from the maximum

Question 14

varying partially distributed load (including where it acts)

Answer 14

splits into two point loads from a rectangle (central) and triangle (1/3 from max.)

W1(rectangle) = ω1(x2-x1)
W2(triangle) = 1/2* (ω2-ω1)*(x2-x1)

Question 15

factor of safety (against overturning)

Answer 15

restoring moment / overturning moment
- RM= Weight * (1/2* dimension of component parallel to force applied)
- OM= Force* distance perp.

Question 16

factor of safety (against sliding)

Answer 16

total reactive forces resisting/ total forces tending to cause it

Question 17

moment of inertia for a circular section

Answer 17

(pi* r^4) / 4 or (pi* d^4)/64

Question 18

moment of inertia for a hollow circular section

Answer 18

(pi* (d^4 - di^4)) / 64

where d = larger diameter and di = inner, smaller diameter

Question 19

modulus of rigidity

Answer 19

shear stress/ shear strain

Question 20

relationship between E, G and v

Answer 20

E = 2G (1 + v)

Question 21

Couple(t)

Answer 21

Force* lever arm

Question 22

angular point load components

Answer 22

Fx = F sin(θ)
Fy = F cos(θ)

Question 23

centroid values for a triangle

Answer 23

y = h/3 and x = b/3

Question 24

Engineer’s theory of bending

Answer 24

M/ I = σ / y

σ = bending stress at distance y = from the neutral axis
M = moment of resistance
I = moment of inertia/ second moment of area about the neutral axis

Question 25

Elastic section modulus

Answer 25

Z = I / y

y = distance from neutral axis to “extreme fibres”
I = moment of inertia

Question 26

Moment of resistance for rectangular sections

Answer 26

(σ* b* d^2)/ 6

where σ is the maximum permissible stress
b = breadth, d = depth

Question 27

shear stress

Answer 27

shear force/ area

Question 28

tensile force (in bending structures)

Answer 28

moment / distance or lever arm