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Lecture 18

Elements of Architectural Structures

ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES:

FORM, BEHAVIOR, AND DESIGN

ARCH 614

DR. ANNE NICHOLS

SPRING 2014

lecture

eighteen

steel construction:

column design Cor-Ten Steel Sculpture By Richard Serra

Museum of Modern Art Fort Worth, TX

(AISC - Steel Structures of the Everyday)

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Lecture 18

Elements of Architectural Structures

ARCH 614

Structural Steel

• standard rolled shapes

(W, C, L, T)

• tubing

• pipe

• built-up

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Lecture 18

Elements of Architectural Structures

ARCH 614

Design Methods (revisited)

• know

– loads or lengths

• select

– section or load

– adequate for

strength and

no buckling

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Lecture 18

Elements of Architectural Structures

ARCH 614

Allowable Stress Design (ASD)

• AICS 9th ed

• slenderness ratio

– for kl/r Cc

22

23

12

..r

Kl

E

SF

fF critical

a

r

Kl

= 126.1 with Fy = 36 ksi

= 107.0 with Fy = 50 ksi

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Lecture 18

Elements of Architectural Structures

ARCH 614

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

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Lecture 18

Elements of Architectural Structures

ARCH 614

Cc and Euler’s Formula

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Lecture 18

Elements of Architectural Structures

ARCH 614

Short / Intermediate

• Le/r < Cc

– where

..2

12

2

SF

F

C

rKl

Fy

c

a

3

3

88

3

3

5..

cc C

rKl

C

rKl

SF

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Lecture 18

Elements of Architectural Structures

ARCH 614

Unified Design

• limit states for failure

1. yielding

2. buckling

gcrnc AFP. 900

ye

y

F.ForF

E.

r

KL440714

n

a

PP

ncu PP

ye

y

F.ForF

E.

r

KL440714

Fe – elastic buckling stress (Euler)

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Lecture 18

Elements of Architectural Structures

ARCH 614

Unified Design

• Pn = FcrAg

– for

– for

– where

ecr

y

F.FF

E.

r

KL8770714

y

F

F

cr

y

F.FF

E.

r

KLe

y

6580714

22

rKL

EFe

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Lecture 18

Elements of Architectural Structures

ARCH 614

Procedure for Analysis

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

2. find Fcr (see Note) from appropriate equation

• tables are available

3. compute Pn = FcrAg

4. is Pa Pn/? or is Pu Pn? • yes: ok

• no: insufficient capacity and no good

Note: text uses Fc

and old = 0.85

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Lecture 18

Elements of Architectural Structures

ARCH 614

Procedure for Design

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 (see Note) from appropriate

equations • or find a chart

4. compute Pn = FcrAg

Note: text uses Fc

and old = 0.85

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Lecture 18

Elements of Architectural Structures

ARCH 614

Procedure for Design (cont’d)

5. is 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

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Lecture 18

Elements of Architectural Structures

ARCH 614

Column Charts, Fcr

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Lecture 18

Elements of Architectural Structures

ARCH 614

Column Charts

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Lecture 18

Elements of Architectural Structures

ARCH 614

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

22

1

rKl

EAPe

factoredmaxu MBM 1

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Lecture 18

Elements of Architectural Structures

ARCH 614

Beam-Column Design

• LRFD (Unified) Steel

– for

– for

Pr is required, Pc is capacity

c – resistance factor for compression = 0.9

c – 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

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Lecture 18

Elements of Architectural Structures

ARCH 614

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

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Lecture 18

Elements of Architectural Structures

ARCH 614

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

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Lecture 18

Elements of Architectural Structures

ARCH 614

Rigid Frame Design (revisited)

• column effective length, k

A

B