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ARCH5023/ARCH4333 -
ARCHITECTURAL STRUCTURES I
][ STEEL
STRUCTURES ][
THE UNIVERSITY OF OKLAHOMA
- COLLEGE OF ARCHITECTURE
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STEEL COLUMNS
WITH BENDING
COLUMNS WITH BENDING
======================
PA 330
=====
Bending in addition to axial compression
=============================
a. eccentricity
due to supports on column face
brackets etc.
b. moment-resistive connection
rigid frame
c. wind = beam load
d. horizontal load
from cars
earth quakes
explosions
Theory:
======
buckling effect of column
combined with
effects of laterally unsupported beam
P-delta effect
PA 230
P-Delta Effect:
===========
(PA 230)
Occurs when the deflection
due to bending
moves the centroid of the column at midheight
away from the line of action
of the axial compression force.
This results in some additional bending moment
of a magnitude equal to the product of
compression force (P)
times the deflection (delta)
The entire moment is a P-delta effect.
Equivalent Design Load
=================
that incorporates the bending effect
=========================
P' = P + BxMx + ByMy
P' = equivalent axial load
P = actual axial load
Bx = bending factor for the section's x-axis
Mx = bending moment about the x-axis
By = bending factor for the section's y-axis
My = bending moment about the y-axis.
Bx & By Table 10.2 PA 321 & 322
Equivalent Design Load
that incorporates the bending effect
EXAMPLE PROBLEM
Equivalent Design Load that incorporates the bending effect
Example Problem:
=============
Equivalent Design Load that incorporates the bending effect
It is desired to use a 10 in W shape
for a column that sustains an
axial compression plus bending.
The axial compression load from above
is 120 kips
and the beam load is 24 kips
with the beam attached at the column face.
The Column is 16 ft high and
has a K factor of 1
Select a trial section for the column
A. GIVEN
10 inch W shaped column
axial compression load from above = 120 kips
beam load = 24 kips
beam attached at the column face.
column height = 16 ft
K factor = 1
B. ASKED
Select a trial section for the column.
C. DIAGRAM
| Pc = 120 kips
|
| | Pb = 24 kips
===
| |
| |_________
| |_________
| |
| |
===
|----|
10"
D. SOLUTION
1. Bending occurs only about the x-axis
only Bx factor is critical
2. Table 10.2 PA 321
scanning the column of Bx factors
observe that factor for 10 W sections
range from 0.261 - 0.2777
3. We have not yet determined the section to be used.
It is necessary to make an assumption
for the factor and verify the assumption
after the selection is made.
Let us assume a Bx of 0.27
4. P' = P + BxMx + ByMy
P' = equivalent axial load
P = actual axial load
Bx = bending factor for the section's x-axis
Mx = bending moment about the x-axis
By = bending factor for the section's y-axis
My = bending moment about the y-axis.
5.
P = P c + P b
P = 120 kips + 24 kips
P = 144 kips
P c = load from column
P b = load from beam
6. Bending occurs only around the x-axis
By = 0
My = 0
7. P' = P + BxMx + ByMy
= 144 kips + 0.27 (Pb x d/2)
Pc + Pb + table 10"/2
P' = (120 + 24 kips) + 0.27 (24 kips) x (5in)
P' = 144 + 32.4
P' = 176.4 kips
8. K L
K = 1 given
L = 16 ft
K L
1 x 16
K L = 16
9. Table 10.2 PA 321
KL = 16
P' = 144 kips
W 10 given
10. W 10 X 45 SELECTED
11. Bx = 0.271
very close to our assumption of 0.27
E. ANSWER
STEEL COLUMNS RELATED SITES
