Architecture 324

Structures II

Steel Beam Analysis and Design

• Steel Properties

• Steel Profiles

• Steel Codes: ASD vs LRFD

• Analysis Method

• Design Method

University of Michigan, TCAUP Structures II Slide 1/28

Cold Form Sections

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Photos by Albion Sections Ltd, West Bromwich, UK

Cold Form Sections

From:

Building Design Using Cold Formed Steel Sections: Structural Design to BS 5950-5:1998. Section Properties and Load Tables. p. 276

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Cold Form Sections

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Hot Rolled Shapes

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Hot Rolled Shapes

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Standard section shapes:

W – wide flange

S – American standard beam

C – American standard channel

L – angle

WT or ST – structural T

STD, XS or XXS – Pipe

HSS – Hollow Structural SectionsRectangular, Square, Round

LLBB , SLBB - Double Angles

Nomenclature of steel shapes

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Castellated Sections:

round

hexagonal

Nomenclature of steel shapes

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Columns:

Closer to squareThicker web & flange

Beams:

Deeper sectionsFlange thicker than web

Steel W-sections for beams and columns

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Columns:

Closer to squareThicker web & flange

Beams:

Deeper sectionsFlange thicker than web

Steel W-sections for beams and columns

Photo by Gregor Y.

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University of Michigan, TCAUP Structures I I Slide 11/28

Young's ModulusYoung's Modulus or the Modulus of Elasticity, is obtained by dividing the stress by the strain present in the material. (Thomas Young, 1807)

It thus represents a measure of the stiffness of the material.

Strain

Stre

ss

Fu

Fy

E

y.001 to .002

u.1 to .2

sh.01 to .03

r.2 to .3

Esh

Developed by Scott CivjanUniversity of Massachusetts, Amherst

University of Michigan, TCAUP Structures I I Slide 12/28

Stress vs. Strain – mild steel

Strain

Stre

ss

E

y.001 to .002

u.1 to .2

sh.01 to .03

r.2 to .3

Esh

Elastic-Perfectly PlasticAssumed in Design

Fu

Fy

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Stress vs. Strain – AISC design curve

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Stress Analysis

Allowable Stress Design (ASD)

• use design loads (no F.S. on loads)

• reduce stress by a Factor of Safety F.S.

Load & Resistance Factored Design (LRFD)

• Use loads with safety factor

• Use factor on ultimate strength

Allowable Flexure Stress

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Steel Beams by ASD

Yield Stress Values• A36 Carbon Steel Fy = 36 ksi• A992 High Strength Fy = 50 ksi

Allowable Flexure Stress• Fb = 0.66 Fy “Increased” • = Lc

– Compact Section

– Braced against LTB (l <Lc)

• Fb = 0.60 Fy “Basic” ° = Lu– Compact or Not

– Lc < l < Lu

• Fb < 0.60 Fy “Decreased”– Compact or Not

– LTB failure mode (l >Lu)

Allowable Shear Stress• Fv = 0.40 Fy

– Fv = V/(twd) lUniversity of Michigan, TCAUP Structures II Slide 16/28

from AISC 9th ed.

Given: allowable stress, steel section

Find: moment or load capacity

1. Find the Section Modulus for the given section from properties tables.

2. Determine the equation for maximum moment in the beam.

3. Assume maximum stress level: fb=Fb

4. Solve the flexure stress equation for moment: M=Fb S

5. Calculate load based on maximum moment.

Capacity Analysis of Steel Beam

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Find Load w in KLFFy = 36 ksi

Fb = 0.66 Fy = 24 KSI

1. Find the Section Modulus for the given section from the tables (D-35 and D-36).

2. Determine the maximum moment equation.

Example – Capacity Analysis of Steel Beam

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3. Using the flexure equation, fb=Fb, solve for the moment, M.

4. Using the maximum moment equation, solve for the distributed loading, W in kips or w in klf.

Example – Load Analysis cont.

W30x116

w = 1.28 KLF

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Beam Design with Section Modulus Table1. Calculate Required Moment 2. Assume Allowable Stress

– Fully bracedFb = 0.66Fy = 24 ksi (A36)

– Partially braced (l < Lu) Fb = 0.60Fy = 21.6 ksi (A36)

3. Using the flexure equation, – set fb = Fb and solve for S

4. Choose a section based on S from the table (D-35 and D-36)

– Bold faced sections are lighter– F’y is the stress up to which the

section is compact (•• is ok for all grades of Fy)

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from Structural Principles, I. Engel

1. Use the maximum moment equation, and solve for the moment, M.

2. Assume unbraced length is less than Lu therefore, Fb = 0.6 Fy = 50 ksi

3. Use the flexure equation to solve for Sx.

Design of Steel Beam

Example

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4. Choose a section based on Sx = 64 in3 from the table (D35 and D36).

5. Most economical section is: W16 x 40Sx = 64.7 in3

Design of Steel Beam

Example

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from Structural Principles, I. Engel

6. Add member self load to M and recheck Fb (here we assume DL is already included)

7. Check shear stress:

Allowable Stress

Fv = 0.40 Fy

Actual Stressfv=V/(twd)

fv ≤ Fv

Design of Steel Beam

Example

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6. Check Deflections:

Calculate actual deflection.

Compare to code limits. If the actual deflection exceeds the code limit, a stiffer section is needed.

Design of Steel Beam(Example cont.)

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from the Standard Building Code

Actual deflection

Code limits

Serviceability limits:

Limits by application

Also more stringent cases:

Machine tolerance – e.g. L/1000

DL deflection can be compensated for by beam camber

Steel Beam

Deflection

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Beam without Camber

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Developed by Scott CivjanUniversity of Massachusetts, AmherstFor AISC

Results in deflection in floor under Dead Load.This can affect thickness of slab and fit of non-structural components.

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Developed by Scott CivjanUniversity of Massachusetts, AmherstFor AISC

Results in deflection in floor under Dead Load.This can affect thickness of slab and fit of non-structural components.

Beam with Camber

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Developed by Scott CivjanUniversity of Massachusetts, AmherstFor AISC

Results in deflection in floor under Dead Load.This can affect thickness of slab and fit of non-structural components.

Cambered beam counteracts service dead load deflection.

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Developed by Scott CivjanUniversity of Massachusetts, AmherstFor AISC