formulas Flashcards
strain =
change in length / original ength
stress =
force (perp.) / cross sectional area
moment of inertia for a rectangular section
bd^3/12
second moment of area
sum of moments of inertia (for sections) + sum of Ah^2 (for sections)
- h = distance from middle of section to (neutral) axis
poisson’s ratio
lateral strain/ axial or longitudinal strain
the neutral axes/ the centroid values
sum of Ay or Ax / sum of areas
- where y and x are the distance from the “reference axis”
elastic or young’s modulus
stress/ strain
condition for determinate structure (supported beams)
no. of reactions is greater than or equal to the no. of equilibrium equations (3 or 4 if internal pin)
condition for determinate strucuture (trusses)
m + r = 2j
- m= members, r = reactions, j = nodes or joints
degree of redundancy
R - E
- R= reactions, E= no. of equilibrium equations
UDL
W = ωL
- ω= unit load, L=length of beam
Partially distributed load
W = ω(x2-x1)
- ω= unit load, x2-x1= length of PDL
varying distributed load (including where it acts)
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
varying partially distributed load (including where it acts)
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)
factor of safety (against overturning)
restoring moment / overturning moment
- RM= Weight * (1/2* dimension of component parallel to force applied)
- OM= Force* distance perp.
factor of safety (against sliding)
total reactive forces resisting/ total forces tending to cause it
moment of inertia for a circular section
(pi* r^4) / 4 or (pi* d^4)/64
moment of inertia for a hollow circular section
(pi* (d^4 - di^4)) / 64
where d = larger diameter and di = inner, smaller diameter
modulus of rigidity
shear stress/ shear strain
relationship between E, G and v
E = 2G (1 + v)
Couple(t)
Force* lever arm
angular point load components
Fy = F sin(θ)
Fx = F cos(θ)
centroid values for a triangle
y = h/3 and x = b/3
Engineer’s theory of bending
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
Elastic section modulus
Z = I / y
y = distance from neutral axis to “extreme fibres” (will be two values for top and bottom sections)
I = moment of inertia
Moment of resistance for rectangular sections
(σ* b* d^2)/ 6
where σ is the maximum permissible stress
b = breadth, d = depth
shear stress
shear force/ area
tensile force (in bending structures)
moment / distance or lever arm
max. BM on simply suported beam
ωL^2 / 8
max. BM for cantilever
ωL^2 / 2
Z(yy) - specific simplification for rectangular sections
bd^2 / 6
