CE
496
Introduction to
Structural Design
Winter 2011
Howard
Lum
February 17, 2011
Agenda
Loads
Tributary Area
Dead Load
Live Load & LL Reduction
Wind Load
Seismic Load
Steel Tension, Compression and Flexural Design
Concrete Basics
Q&A
Loads
CBC Chapter 16 provides the requirements
Dead Loads:
Wt. of Steel = 490
pcf
Wt. of Concrete = 150
pcf
Wt. of Masonry = 115
pcf
Density of Water = 62.4
pcf
Density of Wood = 40
pcf
Live Loads
Live Loads depend on the group of occupancy
Live Loads: See CBC Table 1607.1 (2 pages)
For the County project, special conditions
include:
Handrail design:
Lateral Load = 50
plf
Vehicle Barrier:
Lateral Load = 6,000 lb
Loads are given in pressure (psf)
To convert psf to uniform load W (pounds/ft):
W (#/ft) = Load (psf) x Tributary Width
Example:
LL=60
psf
, beams spaced at 12 ft on center,
span = 40 ft
w
LL
= (60)*12 = 720 lb/ft
A
T
= 12 * 40 = 480 SF
Trib. Width
for Beam A
Beam A
PLAN
Beam & Column Loads
Beam Tributary Area
Column Tributary Area
Live Load Reduction
Floor Live Load Reduction
–
CBC 1607.9
Method 1 (1607.9.1)
LL Reduction if
K
LL
A
T
>= 400 SF
L = Lo (0.25 + 15/√K
LL
A
T
)
Lo: unreduced LL (
psf
)
K
LL:
1

4 (Table 1607.9.1)
A
T
Tributary Area (sq ft)
LL > 100
psf
shall not be reduced EXCEPT:
Member supports 2 or more floors
LL
–
no reduction in public assembly areas
LL Distribution
DL always applies to the entire structure
LL applies to areas of maximum stress:
Simple Span Beam
Overhang Beam
LL
LL
LL
DL
DL
DL
Load Combinations
CBC Section 1605
Strength Design: U <=
Ф
*(Strength)
U = 1.2 (D+F) + 1.6 (L+H)
U = 1.2 D + 1.6 W + 0.5 L
U = 0.9 D + 1.6 W + 1.6H
Working Stress Design:
D + L < (Allowable stress)
–
Not used
Strength Design is based on probabilistic
approach of loads and strength variance
Working Stress Design is based on conventional
elastic stress less than allowable values
Deflection Limits
Allowable deflections in CBC Table 1604.3
Max Deflection = L/360 or L/240 where:
L
=
beam span
Floor LL: L/360
Floor DL+LL: L/240
If L=10 ft, max allow
defl
. = L/240 = 0.5 inch
Use working loads for all deflection calculations
L
Wind Load
CBC Section 1609 and ASCE 7

05 Ch 6
Simplified method: Ps =
λ
*
Kzt
*I * p
s30
where:
λ
is height/exposure factor
Kzt
is
topgraphic
factor (
Eq
6

3)
I is importance factor
P
s30
is pressure at 30 ft, I=1
Other
structures ASCE 6.5.15
F = q
z
GC
f
A
f
where q
z
= velocity pressure, G = 0.85 (rigid
structure), C
f
from Fig. 6

21, A
f
=
proj
. area
Wind Load
Importance Factor I is based on Occupancy
Table 1

1 and Table 6

1
California: basic wind speed = 85 mph
Exposure B, C, D as defined in CBC 1609.4.3
City of Long Beach has special wind provisions
based on geographical locations
General approach
Earthquake Load Design
Maximum Considered Earthquake (MCE)
2% probability of exceedance in 50 years ( or 2,500
years return period)
RP = 1/Pe = 1/(0.02/50) = 2500
All MCE’s are given in the CBC with the latest
update in USGS website
http://earthquake.usgs.gov/hazards/
Spectral Accelerations characterized by:
Ss (short T) and S
1
(long T)
T
L
(transition T)
–
CBC Fig. 22

16
S
S
(short T)
MCE
Acceleration
for T=0.2 sec
S
1
(Long T)
MCE
Acceleration
for T=1 sec
Site Class per CBC
Earthquake Load
Site Class Modifications to MCE
Site Class (A

F) determined by Table 1613.5.2
Hard rock to soft soil
Fa = Short Period Mod. Factor

1613.5.3(1)
Fv = Long Period Mod. Factor

1613.5.3(2)
Design Earthquake:
S
DS
= 2/3 * Fa * Ss
S
D1
= 2/3 * Fv * S
1
Earthquake behavior of Structures
Effective Seismic Weight
W (in seismic analysis):
Weight (DL) of the Diaphragm
Weight (DL) of the Exterior Walls
+ 25% floor LL for Storage Areas
+10 psf floor LL for Partitions
+ weight of permanent equipment
+ 20% of flat roof snow load (> 30 psf)
Reference: ASCE 12.7.2 and 12.14.8.1
Tributary Weights
Base Shear (ASCE 12.8)
V= Cs * W:
Cs = S
DS
/ (R/I)
Max Cs = S
D1
/T(R/I) or S
D1
T
L
/T^2(R/I)
Min Cs = 0.01
Min Cs = 0.5S
1
/(R/I) for S
1
> 0.6
T calculation:
Ta = Ct * h
n
x
Min. T = Cu * Ta where Cu from Table 12.8

1
Reference: ASCE 12.8.1 to 12.8.3
TABLE 11.6

1 SEISMIC DESIGN
CATEGORY BASED ON SHORT PERIOD
RESPONSE ACCELERATION PARAMETER
Value of SDS
Occupancy Category
I or II
III
IV
SDS < 0.167
A
A
A
0.167 ≤
SDS < 0.33
B
B
C
0.33 ≤
SDS < 0.50
C
C
D
0.50 ≤ SDS
D
D
D
Vertical distribution of Forces
Reference: ASCE 12.8.3
F
x
= C
vx
* V
where C
vx
=
w
x
h
x
k
/∑
w
i
h
i
k
V
W
Seismic Load Combination
Load combination w/seismic
Strength Design (12.4.2.3):
(1.2 + 0.2 S
DS
)D +
*Q
E
+ L + 0.2S
(0.9
–
0.2 S
DS
)D +
*Q
E
+ 1.6H
Check both downward seismic and uplift seismic
forces in combination with dead load and live
load
Note: L can be 0.5L (if Lo <= 100psf)
Steel Properties
Es=29,000
ksi
Fy
Fu
1
Steel: Availability of ASTM Grades
58
50
58
Tension Members
Strength Design:
Pu
<=
t *
Pn
Tensile Capacity:
t *
Pn
Failure Modes:
Deformation at yield (gross area)
t = 0.90,
Pn
=
Fy
*Ag
Fracture at tensile strength (net area)
t = 0.75,
Pn
= Fu*
Ae
Yield
Fracture
Compression
–
Stability controls
Elastic Buckling Stress (Euler)
given in AISC
Eq
E3

4
Fe: critical compressive
stress
above which column buckles
Fe
is independent of Fy or Fu
Fe =
π
2
*E/(KL/r)
2
Fcr
= 0.877*Fe
K=1.0
Compression
–
Strength Controls
KL/r <=4.71 √E/
Fy
, column
strength governs (not stability)
Fcr
= [0.658
(Fy/Fe)
]*Fy
where Fe =
π
2
*E/(KL/r)
2
AISC Compression E3
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
0
20
40
60
80
100
120
140
160
180
200
Fe (Euler Critical Stress)
KL/r
Fcr
Fy
=36
ksi
Fy
=50
ksi
Double Sym. Beam Design
AISC Chapter F
b
*
Mn
= 0.9*
Mn
Mn
is dependent on
lateral
unbraced
length
L
b
of the compression
flange
Lateral

torsional
buckling governs
design if L
b
>
Lp
Compression
Flange
L
b

Unbraced
Length
L
b
is independent of the span length
L
b
can be 0 if the compression flange is
continuously braced
Example: Span = 50 ft, L
b
= 25 ft
Steel Beam Design Curve
Concrete Design
ACI 318
Mn
>= Mu where
is 0.9
Vn
=
(
Vc
+Vs) >= Vu where
is 0.75
Pn
>=
Pu
where
is 0.65 to 0.90
f’c
: 28

day compressive strength (3000
–
8000 psi)
Fy
: Yield strength of reinforcement (60
ksi
)
Questions & Answers
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