Beams

BEAMS

A structural member loaded in the transverse direction to the longitudinal axis.

Internal Forces:Bending Moments and Shear

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Stability

Structural Steel - Characteristics

Buckling: Instability due to slenderness

Stability

Elastic Buckling

Limit States

Load Deflection

0

50

100

150

200

250

300

350

400

450

500

0 4 8 12 16 20 24

Deflection (in)

Lo

ad

(k

ips

)

FEM Test

Limit States

Limit States

Limit States

Classification of Shapes

Compact Section

Non-Compact Section

Web Local Buckling

Flange Local Buckling

Bending Strength of Compact Shapes

Lateral Torsional Buckling

Bending Strength of Compact Shapes

yyp F

ErL 76.1

Bending Strength of Compact Shapes

Laterally Supported Compact Beams

xypn ZFMM

yypb F

ErLL 76.1

Bending Strength of Compact Shapes

Bending Strength of Compact Shapes

Elastic Buckling

pxcrn MSFM

27.0

76.6117.0

95.1

EJc

hSF

hS

Jc

F

ErLL oxy

oxytsrb

2

2

2

078.01

ts

b

oxtsb

bcr r

L

hS

Jc

rL

ECF

xyr SFM 7.0

Elastic Buckling

Cb = factor to account for non-uniform bending within the unbraced length

L/4 L/4 L/4 L/4

A B C

Mmax

0.33435.2

5.12

max

max

mCBA

b RMMMM

MC

See AISC table 3-1 p 3.10

Elastic Buckling

Elastic Buckling

Elastic Buckling

Cb = factor to account for non-uniform bending within the unbraced length

0.33435.2

5.12

max

max

mCBA

b RMMMM

MC

Rm= 1 for doubly symmetric cross sections and singly symmetric subject to single curvature

See textbook p 190 for other cases

Elastic Buckling

Cb = factor to account for non-uniform bending within the unbraced length

2

2

2

078.01

ts

b

oxtsb

bcr r

L

hS

Jc

rL

ECF

Elastic Buckling

Cb = factor to account for non-uniform bending within the unbraced length

x

wyts S

CIr 2

channelsfor

2

shapes I symmetricdoubly for 1

w

yo

C

Ihc

ho = distance between flange centroids = d-tf

Bending Strength of Compact Shapes

Bending Strength of Compact Shapes

Inelastic Buckling

ppr

pbrppbn M

LL

LLMMMCM

rbp LLL

xyr SFM 7.0

Linear variation between Mp and Mr

Nominal Flexural Strength – Compact Shapes

2

2

2

078.01

ts

b

oxtsb

bcr r

L

hS

Jc

rL

ECF

rbp

brpxcr

ppr

pbrppb

pbp

n LLL

LLMSF

MLL

LLMMMC

LLM

M

for

for

for

Nominal Flexural Strength – NON-Compact Shapes

Most W- M- S- and C- shapes are compact

A few are NON-compact

NONE is slender

Webs of ALL hot rolled shapes in the manual are compactFLB and LTB

Built-Up welded shapes can have non-compact or slender websFLB, WLB, LTB (AISC F4 and F5)

Nominal Flexural Strength – NON-Compact Shapes

for Manualin shapes rolledfor /A

for

for

br

rpppr

prpp

pp

n

N

MMMM

M

M

WLB

t

bλ

f

f

2

F

Eλ

yp 38.0

F

Eλ

yr 0.1