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4.440 / 4.462 Basic Structural Design
Spring 2009
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Basic Structural Design
J.A. Ochsendorf
Spring 2009
MIT Architecture
EQUATIONS FOR STRUCTURAL DESIGN
Axial stress: σ = P/A
Bending stress due to an applied moment, M: σ = My/I
where y is the distance from the neutral axis of the beam
Critical buckling load for a column in axial compression: Pcr = π2EI/(kL)2
b
Moment of Inertia (I):
y
x
y
x
d
x
x
y
y
Ixx = Iyy = πd4/64
•
Ixx = bh3/12
Iyy = hb3/12
Modulus of Elasticity (E): Approximate values for six common structural materials:
Esteel = 29,000 ksi
Econcrete = 3,000 ksi
•
h
Eglass = 10,000 ksi
Etimber = 1,600 ksi
Ealuminum = 10,000 ksi
Ebrick = 3,000 ksi
Effective Length of the column (k):
(a)
(b)
0.5
0.7
(c)
(d)
(e)
(f)
Buckled shape of
column is shown by
dashed line
Theoretical K value
End-condition code
1.0
1.0
2.0
Rotation fixed
Translation fixed
Rotation free
Translation fixed
Rotation fixed
Translation free
Rotation free
Translation free
2.0
Figure by MIT OpenCourseWare.
Effective Length Factors k for centrally loaded columns with various idealized end conditions.
(*)
(*)
Taken from: Basic Steel Design with LRFD, T.V. Galambos, F.J. Lin and B.G. Johnston, Prentice Hall, Upper Saddle River, New Jersey,
1996, pp. 88-89.