seventeen pipe built-up steel construction: columns & tension - - PowerPoint PPT Presentation

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seventeen

steel construction: columns & tension members

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN ARCH 331

• DR. ANNE NICHOLS

SUMMER 2018

Steel Columns & Tension 1 Lecture 17 Architectural Structures ARCH 331

lecture

Cor-Ten Steel Sculpture By Richard Serra Museum of Modern Art Fort Worth, TX (AISC - Steel Structures of the Everyday)

F2008abn Steel Columns & Tension 2 Lecture 20 Architectural Structures ARCH 331

Structural Steel

• standard rolled shapes

(W, C, L, T)

• tubing
• pipe
• built-up

F2008abn 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

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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

2

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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 

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Cc and Euler’s Formula

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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   

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Unified Design

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

Fe – elastic buckling stress (Euler)

Steel Columns & Tension 8 Lecture 17 Architectural Structures ARCH 331

n c u

P P  

4.71 2.25

y c y e

F L E or r F F   4.71 2.25

y c y e

F L E or r F F  

 

n a

P P

g cr n c

A F P .   90 

3

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Unified Design

• Pn = FcrAg

– for – for – where

Steel Columns & Tension 9 Lecture 17 Architectural Structures ARCH 331

4.71 0.658

y e

F F c cr y y

L E F F r F          

4.71 0.877

c cr e y

L E F F r F  

2 2 e c

E F L r        

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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

Steel Columns & Tension 10 Lecture 17 Architectural Structures ARCH 331 F2011abn

• 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 (or Pn/ = FcrA)
• r Pn = FcrAg
• r find factual = P/A

Procedure for Design

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Procedure for Design (cont’d)

• 5. is P  Pallowable? 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.

Steel Columns & Tension 12 Lecture 17 Architectural Structures ARCH 331

% P P

c r 100



4

F2008abn Steel Columns & Tension 11 Lecture 20 Architectural Structures ARCH 331

Column Charts, Fa (pg. 461-462)

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Column Charts, Fcr

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Column Charts

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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

Lc1 – effective length in plane of bending Pe1 – Euler buckling strength  - 1.00 (LRFD), 1.60(ASD)

Steel Columns & Tension 15 Lecture 17 Architectural Structures ARCH 331

m 1 u e1

C B 1 ( P / P )   

1 r nt

M B M 

 

2 1 2 1 e c

EI P L  

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Beam-Column Design

• LRFD (Unified) Steel

– for – for Pr is required, Pc is capacity Mrx is required, Mcx is capacity Mry is required, Mcy is capacity

Steel Columns & Tension 16 Lecture 17 Architectural Structures ARCH 331

8 0.2: 1.0 9

ry rx r r c c cx cy

M M P P P P M M             0.2: 1.0 2

ry rx r r c c cx cy

M M P P P P M M            

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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

F2008abn 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     

F2008abn Steel Columns & Tension 20 Lecture 20 Architectural Structures ARCH 331

Rigid Frame Design (revisited)

• column effective length, k

A B

6

F2008abn Steel Columns & Tension 19 Lecture 20 Architectural Structures ARCH 331

Tension Members

• steel members can

have holes

• reduced area
• increased stress

(AISC - Steel Structures of the Everyday)

g s t A A A

holes all

• f

g n

4    

F2008abn Steel Columns & Tension 20 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 

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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)

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n t u

P P  

g y n t

A F P .   90 

e u n t

A F P .   75 

 

n a

P P