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E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS S PRING 2019 lecture eighteen steel construction: column design Cor-Ten Steel Sculpture By Richard Serra Museum of Modern Art Fort Worth, TX

SLIDE 1

S2019abn Steel Columns 1 Lecture 18 Elements of Architectural Structures ARCH 614

ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 614

DR. ANNE NICHOLS

SPRING 2019 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)

SLIDE 2

S2019abn Steel Columns 2 Lecture 18 Elements of Architectural Structures ARCH 614

Structural Steel

standard rolled shapes

(W, C, L, T)

tubing
pipe
built-up

SLIDE 3

S2019abn Steel Columns 3 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

SLIDE 4

S2019abn Steel Columns 4 Lecture 18 Elements of Architectural Structures ARCH 614

Allowable Stress Design (ASD)

AICS 9th ed
slenderness ratio

– for kl/r  Cc

 

2 2

23 12 . . r Kl E S F f F

critical a

  

r Kl

= 126.1 with Fy = 36 ksi = 107.0 with Fy = 50 ksi

SLIDE 5

S2019abn Steel Columns 5 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 c

F E C

2 

SLIDE 6

S2019abn Steel Columns 6 Lecture 18 Elements of Architectural Structures ARCH 614

Cc and Euler’s Formula

SLIDE 7

S2019abn Steel Columns 7 Lecture 18 Elements of Architectural Structures ARCH 614

Short / Intermediate

Le/r < Cc

– where

 

. . 2 1

2 2

S F F C r Kl F

y c a

           

   

3 3

8 8 3 3 5 . .

c c

C r Kl C r Kl S F   

SLIDE 8

S2019abn Steel Columns 8 Lecture 18 Elements of Architectural Structures ARCH 614

Unified Design

limit states for failure
1. yielding
2. buckling

g cr n c

A F P .   90 

y e y

F . F

F E . r KL 44 71 4  

 

n a

P P

n c u

P P  

y e y

F . F

F E . r KL 44 71 4  

Fe – elastic buckling stress (Euler)

SLIDE 9

S2019abn Steel Columns 9 Lecture 18 Elements of Architectural Structures ARCH 614

Unified Design

Pn = FcrAg

– for – for – where

e cr y

F . F F E . r KL 877 71 4  

y F F cr y

F . F F E . r KL

e y

          658 71 4

 

2 2

r KL E Fe  

SLIDE 10

S2019abn Steel Columns 10 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

SLIDE 11

S2019abn Steel Columns 11 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

r find a chart
4. compute Pn = FcrAg

Note: text uses Fc and old = 0.85

SLIDE 12

S2019abn Steel Columns 12 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



SLIDE 13

S2019abn Steel Columns 13 Lecture 18 Elements of Architectural Structures ARCH 614

Column Charts, Fcr

SLIDE 14

S2019abn Steel Columns 14 Lecture 18 Elements of Architectural Structures ARCH 614

Column Charts

SLIDE 15

S2019abn Steel Columns 15 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  - 1.00 (LRFD), 1.60(ASD)

 

2 2 1

r Kl EA P

 

factored max u

M B M





m 1 u e1

C B 1 ( P / P )   

SLIDE 16

S2019abn Steel Columns 16 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

1 9 8 2 . M M M M P P : . P P

nx b ux nx b ux n c u c r

               1 2 2 . M M M M P P : . P P

nx b ux nx b ux n c u c r

              

SLIDE 17

S2019abn Steel Columns 17 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

SLIDE 18

S2019abn Steel Columns 18 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

l EI l EI G     

SLIDE 19

S2019abn Steel Columns 19 Lecture 18 Elements of Architectural Structures ARCH 614

Rigid Frame Design (revisited)

column effective length, k

A B