CONCRETE STRUCTURES
CONCRETE STRUCTURES 
PROBLEM STATEMENT:
Design a slender column.
Given is a tied column,
which is a member of a braced frame.
The factored moments shown
produce bending about the y-y axis.
Moments about the x-x axis are zero.
lu = 16 feet
Pu = 250 kips top
Pu = 250 kips bottom
Mu = 60 ft kips top
Mu = 10 ft kips bottom
The effective length factor
k equals 0.9 with regards
to bending about the y-y axis, and
k equals 0.85 with respect
to bending about the x-x axis.
Determine the longitudinal reinforcement required
to support the factored loads.
Only 3000 psi concrete is available.
Use Grade 60 rebar.
The ratio of
factored axial dead load to
factored axial total load is
0.6
12" x 14" cross section pre-selected
Pu = 250 kips
Mu = 60 ft kips
lu = 16'
14"
Pu = 250 kips
Mu = 10 ft kips
12"
14"
lu = 16 feet
Pu = 250 kips top
Pu = 250 kips bottom
Mu = 60 ft kips top
Mu = 10 ft kips bottom
k = 0.9 y-y axis
k = 0.85 x-x axis
fc = 3,000 psi = 3 kips/sqin
fy = 60,000 psi = 60 kips/sqin
d = 0.6
ratio of area of reinforcement
terminated to total area of reinforcement
12" x 14" cross section pre-selected
x = 14" = h
y = 12"
y = 12"
x
= 14"
B. ASKED:
longitudinal reinforcement required
number of bars
bar sizes
ties
14"
?
?
12" ?
C. GRAPH: =========
Step (#) by Step (#) Solution =======================
D. SOLUTION:
#1.
The strength of the column will be checked independently for
bending about both principal axes.
#2.
Bending about the y-y axis
Figure 7.9 page 299 Leet
does not apply
0.9 was previously calculated for a
braced frame
= k * lu
r
k = 0.9
<.p>
#3.
r = 0.3 * y
#4.
= k * lu
r
= 0.9 * 16 ft * 12
0.3 * 14 in
= 41.14
=======
= 34 - 12 M1t top = given
M2b bottom = given
34 - (12 -10)
60
34 - (12 * (-)0.1666)
34 - (-2)
36
==
36 < 41.14
The column is long
consider secondary moments
Bending about the y-y Axis
= k * lu
r
k = 0.85 given
r = 0.3 * x
= k * lu
r
= 0.85 * 16 * 12
0.3 *12
= 45.3
=====
34 - 12 M1
M2
34 - 12 0
M2
34 - 0
= 34
====
34 < 45.3
The column is long
consider secondary moment
Analysis for bending about the y-y axis
Design for:
M1b = -10 ft kips
M2b = 60 ft kips
