steel construction: columns & tension...

F2013abn Steel Columns & Tension 1

Lecture 20

Architectural Structures

ARCH 331

lecture

twenty

steel construction:

columns & tension members

Cor-Ten Steel Sculpture By Richard Serra

Museum of Modern Art Fort Worth, TX

(AISC - Steel Structures of the Everyday)

ARCHITECTURAL STRUCTURES:

FORM, BEHAVIOR, AND DESIGN

ARCH 331

DR. ANNE NICHOLS

FALL 2013


Lecture 20


ARCH 331

Structural Steel

• standard rolled shapes

(W, C, L, T)

• tubing

• pipe

• built-up


Lecture 20


ARCH 331

Design Methods (revisited)

• know

– loads or lengths

• select

– section or load

– adequate for

strength and

no buckling


Lecture 20


ARCH 331

Allowable Stress Design (ASD)

• AICS 9th ed

• slenderness ratio

– for kl/r Cc = 126.1 with Fy = 36 ksi

= 107.0 with Fy = 50 ksi

22

23

12

..r

K l

E

SF

fF cr i t ica l

a

r

Kl


Lecture 20


ARCH 331

Cc and Euler’s Formula

• Kl/r < Cc

– short and stubby

– parabolic transition

• Kl/r > Cc

– Euler’s relationship

– < 200 preferred

y

cF

EC

22


Lecture 20


ARCH 331

Cc and Euler’s Formula


Lecture 20


ARCH 331

Short / Intermediate

• Le/r < Cc

– where

..2

12

2

SF

F

C

rKl

Fy

c

a

3

3

88

3

3

5..

cc C

rK l

C

rK l

SF

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Unified Design

• limit states for failure

1. yielding

2. buckling

Fe – elastic buckling stress (Euler)

Steel Columns & Tension 8

Lecture 20


ARCH 331

gc rnc AFP. 9 00

na

PP

ncu PP

ye

y

F.ForF

E.

r

KL440714

ye

y

F.ForF

E.

r

KL440714

F2013abn

Unified Design

• Pn = FcrAg – for

– for

– where


Lecture 20


ARCH 331

y

F

F

cr

y

F.FF

E.

r

KLe

y

6580714

ecr

y

F.FF

E.

r

KL8770714

22

rKL

EFe


Lecture 20


ARCH 331

Procedure for Analysis

1. calculate KL/r • biggest of KL/r with respect to x axes and y axis

2. find Fa or Fcr from appropriate equation • tables are available

3. compute Pallowable = FaA or Pn = FcrAg • or find factual = P/A

4. is P Pallowable (Pa Pn/)? or is Pu Pn? • yes: ok

• no: insufficient capacity and no good

F2013abn

1. guess a size (pick a section)

2. calculate KL/r • biggest of KL/r with respect to x axes and y axis

3. find Fa or Fcr from appropriate equations • or find a chart

4. compute Pallowable = FaA (Pn/ = FcrAg)

or Pn = FcrAg • or find factual = P/A


Lecture 20


ARCH 331

Procedure for Design


Lecture 20


ARCH 331

Procedure for Design (cont’d)

5. is P Pallowable (Pa Pn/)? or is Pu Pn? • yes: ok

• no: pick a bigger section and go back to step 2.

6. check design efficiency

• percentage of stress =

• if between 90-100%: good

• if < 90%: pick a smaller section and

go back to step 2.

%P

P

c

r 100


Lecture 20


ARCH 331

Column Charts, Fa (pg. 361-364)


Lecture 20


ARCH 331

Column Charts, Fcr


Lecture 20


ARCH 331

Column Charts


Lecture 20


ARCH 331

Beam-Column Design

• moment magnification (P-)

Cm – modification factor for end conditions

= 0.6 – 0.4(M1/M2) or

0.85 restrained, 1.00 unrestrained

Pe1 – Euler buckling strength

)P/P(

CB

eu

m

1

11

f a c t o r e dm a xu MBM 1

22

1

rKl

EAPe


Lecture 20


ARCH 331

Beam-Column Design

• LRFD (Unified) Steel

– for

– for

Pr is required, Pc is capacity

c - resistance factor for compression = 0.9

b - resistance factor for bending = 0.9

019

820 .

M

M

M

M

P

P:.

P

P

nxb

ux

nxb

ux

nc

u

c

r

012

20 .M

M

M

M

P

P:.

P

P

nxb

ux

nxb

ux

nc

u

c

r


Lecture 20


ARCH 331

Design Steps Knowing Loads (revisited)

1. assume limiting stress

• buckling, axial stress,

combined stress

2. solve for r, A or S

3. pick trial section

4. analyze stresses

5. section ok?

6. stop when section is ok


Lecture 20


ARCH 331

Rigid Frame Design (revisited)

• columns in frames

– ends can be “flexible”

– stiffness affected by beams and column = EI/L

– for the joint • lc

is the column length of each column

• lb is the beam length of each beam

• measured center to center

b

c

lEI

lEI

G


Lecture 20


ARCH 331

Rigid Frame Design (revisited)

• column effective length, k

A

B

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• steel members can

have holes

• reduced area

• increased stress


Lecture 20


ARCH 331

Tension Members

(AISC - Steel Structures of the Everyday)

g

stAAA holesallofgn

4

2


Lecture 20


ARCH 331

Effective Net Area

• likely path to “rip” across

• bolts divide transferred force too

• shear lag UAA ne


Lecture 20


ARCH 331

Tension Members

• limit states

for failure

1. yielding

2. rupture*

Ag - gross area

Ae - effective net area

(holes 1/8” + d)

Fu = the tensile strength

of the steel (ultimate)

n

a

PP

ntu PP

gynt AFP. 9 00

eunt AFP. 7 50

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