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S2018abn 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

SPRING 2018

S2018abn Steel Columns & Tension 2 Lecture 20 Architectural Structures ARCH 331

Structural Steel

• standard rolled shapes

(W, C, L, T)

• tubing
• pipe
• built-up

S2018abn Steel Columns & Tension 3 Lecture 20 Architectural Structures ARCH 331

Design Methods (revisited)

• know

– loads or lengths

• select

– section or load – adequate for strength and no buckling

S2018abn Steel Columns & Tension 4 Lecture 20 Architectural Structures 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

 

2 2

23 12 . . r Kl E S F f F

critical a

  

r K l

S2018abn Steel Columns & Tension 5 Lecture 20 Architectural Structures ARCH 331

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

2 

S2018abn Steel Columns & Tension 6 Lecture 20 Architectural Structures ARCH 331

Cc and Euler’s Formula

S2018abn Steel Columns & Tension 7 Lecture 20 Architectural Structures ARCH 331

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 K l C r K l S F   

S2018abn

Unified Design

• limit states for failure
• 1. yielding
• 2. buckling

Fe – elastic buckling stress (Euler)

Steel Columns & Tension 8 Lecture 20 Architectural Structures ARCH 331

g c r n c

A F P .   9 0 

 

n a

P P

n c u

P P  

y e y

F . F

• r

F E . r KL 44 71 4  

y e y

F . F

• r

F E . r KL 44 71 4  

S2018abn

Unified Design

• Pn = FcrAg

– for – for – where

Steel Columns & Tension 9 Lecture 20 Architectural Structures ARCH 331

y F F cr y

F . F F E . r KL

e y

          658 71 4

e cr y

F . F F E . r KL 877 71 4  

 

2 2

r KL E Fe  

S2018abn Steel Columns & Tension 10 Lecture 20 Architectural Structures 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 = FaA or Pn = FcrAg
• r find factual = P/A
• 4. is P  Pallowable (Pa  Pn/)? or is Pu  Pn?
• yes: ok
• no: insufficient capacity and no good

S2018abn

• 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
• r find a chart
• 4. compute Pallowable = FaA (Pn/ = FcrAg)
• r Pn = FcrAg
• r find factual = P/A

Steel Columns & Tension 11 Lecture 20 Architectural Structures ARCH 331

Procedure for Design

S2018abn Steel Columns & Tension 12 Lecture 20 Architectural Structures 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



S2018abn Steel Columns & Tension 13 Lecture 20 Architectural Structures ARCH 331

Column Charts, Fa (pg. 461-462)

S2018abn Steel Columns & Tension 14 Lecture 20 Architectural Structures ARCH 331

Column Charts, Fcr

S2018abn Steel Columns & Tension 15 Lecture 20 Architectural Structures ARCH 331

Column Charts

S2018abn Steel Columns & Tension 16 Lecture 20 Architectural Structures 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  - 1.00 (LRFD), 1.60(ASD) m 1 u e1

C B 1 ( P / P )   

fa cto r ed m a x u

M B M





1

 

2 2 1

r Kl EA P

e

 

S2018abn Steel Columns & Tension 17 Lecture 20 Architectural Structures 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

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

              

S2018abn Steel Columns & Tension 18 Lecture 20 Architectural Structures 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

S2018abn Steel Columns & Tension 19 Lecture 20 Architectural Structures 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

l EI l EI G     

S2018abn Steel Columns & Tension 20 Lecture 20 Architectural Structures ARCH 331

Rigid Frame Design (revisited)

• column effective length, k

A B

S2018abn

• steel members can

have holes

• reduced area
• increased stress

Steel Columns & Tension 21 Lecture 20 Architectural Structures ARCH 331

Tension Members

(AISC - Steel Structures of the Everyday)

2

4

n g

• f all holes

s A A A t g    

S2018abn Steel Columns & Tension 22 Lecture 20 Architectural Structures ARCH 331

Effective Net Area

• likely path to “rip” across
• bolts divide transferred force too
• shear lag

U A A

n e 

S2018abn Steel Columns & Tension 23 Lecture 20 Architectural Structures 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

• f the steel (ultimate)

 

n a

P P

n t u

P P  

g y n t

A F P .   9 0 

e u n t

A F P .   7 5 