General Design Principles for DuPont Engineering Polymers - Module

In equation form,
P CR = π2 E I
2
E = Tangent modulus at stress
and is called the Euler Formula for round ended
columns.
h
b
2
y1
y2
Form of section Area A
h
b
H
h
y 1
y 2
d h
H
b
2
B
h
b
B
B
b
2
b
2
b
H
H
C
H
h
θ
y 2
y 1
H
H
B
2
B
2
b y1 h
h
B B
B1
2
a
b
2
b
B
b
2
a
B
b
d h h1 d1
H
B1
2
b
2
h
a 1 1
d
d
A = bh y 1 = y 2 =
A = BH + bh
b
y 1
y 2
y 2
A = BH – bh
A = bd1 + Bd
+ H(h + h1 )
A = Bh – b(H – d)
H
a
2
B B
A = a 2
b
d
y1 = y2 = H
2
y 1 = y 2 = H
2
y 1 = H – y 2
y 1 = y 2 = 1 a
2
Table 4.01. Properties of Sections
h cos θ + b sin θ
2
y 2 = 1 aH 2 + B1d 2 + b1d1 (2H – d1 )
2 aH + B1d + b1d1
y 1 = H – y 2
Distance from
centroid to extremities
of section y1, y2
y 2 = 1aH 2 + bd 2
2(aH + bd)
y
1 A = bd
d 1 1 y1 = y2 = 1 d
2
b
y 2
y 1
y 2
a
2
H
y 1
y 2
16
Thus, if the value for PCR is less than the allowable
load under pure compression, the buckling formula
should be used.
If the end conditions are altered from the round ends,
as is the case with most plastic parts, then the PCR load
is also altered. See Table 4.04 for additional end
effect conditions for columns.
Moments of inertia I1 and I2
about principal
central axes 1 and 2
I 1 = bh (h 2 cos 2 + b 2 sin 2
12
I1 = BH 3 + bh 3
12
I 1 = BH 3 – bh 3
12
I 1 = I 2 = I 3 = 1 a 4
12
θ )
I 1 = 1 (By 3 –B 1 h 3 + by 3 – b 1 h 3 )
3 2 1 1
I 1 = 1 (By 3 –bh 3 + ay 3 )
3 2 1
I 1 = 1 bd 3
12
θ
r1 = √ (h2
cos 2 θ + b θ
2 sin 2
)
12
r1 = √ BH 3 + bh 3
12 (BH + bh)
r 1 = √ BH 3 – bh 3
12 (BH – bh)
r1 =
I
√(Bd
+ bd1 ) + a(h + h1 )
r 1 = √
Radii of gyration r1 and r2
about principal
central axes
I
Bd + a(H – d)
r 1 = r 2 = r 3 = 0.289a
r 1 = 0.289d