Struts Flashcards
Euler’s Formula to calculate critical load
Pcr = (π^2 E I) / L^2
Pcr = critical load
E = elastic modulus
I = second moment of area
L = effective length
when the slenderness ratio is less than 100, Pcr = σcr A can be used
Calculate the Factor of safety
η = Pcr / P
Pcr = critical load
P = current load
Effective Lengths for different beams
Pin-Ends: Le = L
Free End to Fixed: Le = 2L
Fixed Ends: Le = L/2
Fixed to Pin: 0.7L
Minimum second moment of area
The axes most likely to bend
find the moment of inertia
rectangle:
Ix = bh^3/12 + Ad^2
Iy = b^3h/12
circle:
I = πd^2/4
base, x-axis (b)
height, y-axis (h)
area (A)
distance from the neutral axis to the centroid (d)
slenderness ratio
rx = sqrt(Ix/A)
ry = sqrt(Iy/A)
measure of a column’s vulnerability to buckling
critical stress
σcr = (π^2 E) / (L / r)^2
slenderness (L/r)
elastic modulus (E)
second moment of area (I)
effective length (L)
find the maximum stress (σmax) in a column experiencing eccentric loading
= P/A (1 + (ymax + e)c/r^2 )
= P/A (1 + ec/r sec(sqrt(P/EA) L/2r) )
radius of gyration (r)
eccentricity of the load, distance of P from centroid (e)
maximum radius (c)
max deflection (ymax)
load applied (P)
youngs modulus (E)
length (L)
moment of inertia (I)
radius of gyration
r = sqrt(I/A)
moment of inertia (I)
area (A)
how “spread out” the material is from the axis
max deflection (ymax)
ymax = e( sec(sqrt(P/EI) L/2) - 1)
eccentricity of the load, distance of P from centroid (e)
load applied (P)
youngs modulus (E)
length (L)
moment of inertia (I)
greatest vertical displacement a structure undergoes under load
eccentricity ratio
= ec/r^2
eccentricity ratio becomes insignificant for large struts, have a slenderness ratio larger than that of 100
measures how off-centre a load is applied to a column or strut
