formulas/ methods

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 VDL

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

Fy = F sin(θ)
Fx = 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" (will be two values for top and bottom sections) 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

Question 29

max. BM on simply suported beam

Answer 29

ωL^2 / 8

Question 30

max. BM for cantilever

Answer 30

ωL^2 / 2

Question 31

Z(yy) - specific simplification for rectangular sections

Answer 31

bd^2 / 6

Question 32

deflection differential equation

Answer 32

EI * d^2y/dx^2 = M

Question 33

What would be the moment function for a simply supported beam with a UDL

Answer 33

M = ((w*L)/2)*x - (w*x)*(x/2) - at distance x from support (reaction for support and moment of UDL along distance x)

Question 34

when integrating never forget... (3 things)

Answer 34

verify the moment function verify boundary conditions don't forget to include constants in integration (indefinite integral)

Question 35

maximum deflection for UDL simply supported beam

Answer 35

- 5 w L^4 / 384 EI where w is in N/m

Question 36

maximum slope for UDL simply supported beam

Answer 36

-w L^3 / 24 EI

Question 37

steps to writing the moment function

Answer 37

for uniform load one general formula can be deduced with point loads/ multiple loads, multiple sections should be considered with different functions e.g. when x < 4m

Question 38

when integrating via successive integration or McCauley's method, how do constants appear?

Answer 38

+ Ax + B

Question 39

How can constants be solved when multiple functions are in use?

Answer 39

Equate the slope and deflection equations at the "overlap" boundary value

Question 40

Deflections are frequently left in terms of ___ and _____.

Answer 40

E and I (modulus of elasticity and moment of inertia)

Question 41

A singularity function

Answer 41

(x - a)

Question 42

McCauley's moment function

Answer 42

Mx = R(A)*x - W*(x - a)

Question 43

how should the singularity function be integrated

Answer 43

must be continually enclosed by square brackets and integrated as such without expanding

Question 44

rotation couple (representation in McCauley's method)

Answer 44

(x - a)^0

Question 45

on a cantilever, a UDL singularity function will be ______________.

Answer 45

raised to the power of 2 (consider under and above the beam)

Question 46

@ULS (load factor design)

Answer 46

1.35*(permanent actions) + 1.5*(variable actions)

Question 47

@SLS

Answer 47

(permanent actions) + (variable actions)

Question 48

In bending checks, ___ loading will be used. In deflection calculations, ____ is used

Answer 48

ULS, SLS

Question 49

SW of steel (standard)

Answer 49

0.25kN/m

Question 50

maximum deflection for central PL simply supported beam

Answer 50

P L^3 / 48 E I

Question 51

in a stress distribution diagram, the arrows act _______ the parallel centre line.

Answer 51

towards