# Introduction to Structural Design

Urban and Civil

Nov 26, 2013 (4 years and 5 months ago)

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CE
496

Introduction to
Structural Design

Winter 2011

Howard
Lum

February 17, 2011

Agenda

Tributary Area

Steel Tension, Compression and Flexural Design

Concrete Basics

Q&A

CBC Chapter 16 provides the requirements

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 depend on the group of occupancy

Live Loads: See CBC Table 1607.1 (2 pages)

For the County project, special conditions
include:

Handrail design:

plf

Vehicle Barrier:

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 Tributary Area

Column Tributary Area

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

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

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

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

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

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

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

Note: L can be 0.5L (if Lo <= 100psf)

Steel Properties

Es=29,000
ksi

Fy

Fu

1

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
)