1

BEAM-COLUMNS

PROF. V. KALYANARAMAN

Department of Civil Engineering

Indian Institute of Technology MadrasChennai 600036

email: kalyan@civil.iitm.ernet.in

2

DESIGN OF BEAM COLUMNSINTRODUCTION

SHORT & LONG BEAM-COLUMNS Modes of failure

Ultimate strength

BIAXIALLY BENT BEAM-COLUMNS

DESIGN STRENGTH EQUATIONS

Local Section Flexural Yielding

Overall Member Flexural Buckling

STEPS IN ANALYSING BEAM-COLUMNS

ANALYSIS EXAMPLE

SUMMARY

3

INTRODUCTIONCauses Of Bending In Beam Columns

x

y z

Eccentric CompressionJoint Moments in Braced Frames Rigid Sway Moments in Unbraced FramesBiaxial Moments in Corner Columns of Frames

4

SHORT BEAM-COLUMNS

Pcs = Ag * fy MP = Z * fy

P=

Pcs

Axial compression

MP

Bending moment

Fc MCombined compression and bending, P & M

fy

fy fy

fy

fy

fy fy

fy

fy

+M

5

SHORT BEAM-COLUMNS

Failure envelope

1.0

O 1.0Mo/Mp Mmax/Mp M/Mp

Short columnloading curve

Fcl /Pcs

F0/Pcs

Fc/Pcs

Eqn. 3

M / MP 1.0

Fc / Pcs + 0.85 M / MP 1.0Eqn 3

6

LONG BEAM COLUMNS

LinearNon-Linear

0

M0

P *

M0

Non – Sway Frame

7

LONG BEAM-COLUMNS

Sway Frames

0

M0

M

8

LONG BEAM-COLUMNS

BM0

0.5

0.8

P/Pcr = 0.0

1.0

0.8

O

1.0

P .Pcr

M0/MP= 0.0

A

0.10.5

E

0

PP1

E

0

PP1

E

0mmax

PP1

MCM

9

LONG BEAM-COLUMNS

Long columnsloading curve

Short columnloading curve

Fcl /Pcs

F0/Pcs

Fc/Pcs

Eqn. 3

Failure Envelope

Mo/Mp Mmax/Mp

M / MP

1.0

1.0

10

SLENDER BEAM-COLUMNS

AAfter correction for (P-) effect

Fc/Pcs

Fcl/Pcs

My/Mpy

Short column failure envelope

After correcting for sway and bow (P- and P-)

1.0

1.0

P*

P*

Minor axis bending

1.0

Major axis bending

Mx/Mpx

Fc/Pcs

Fcl/Pcs

After correction for (P-) effect

Short column failure envelope

After correcting for sway and bow (P- and P-)

1.0

Uniaxial Bending

11

SLENDER BEAM-COLUMNS

A

Mx

Mpx

P/Py < 0.25

P/Py >0.5

Short Column

Slender Column

Fig. 7 Beam-column Moment Rotation BehaviourO

BC

C’

FF’

F’’

E

D

12

BEAM-COLUMNS / BIAXIAL BENDING

Fcl/Pcs

My/ MpyMx/Mpx

Fig. 8 beam-columns under Biaxial Bending

/r = 0

/r increases

13

DESIGN STRENGTH EQUATIONS

Local Section Failure

Overall Member failure

0.1fZ

M

fZ

M

fA ydy

y

ydx

x

ydg

F c

0.1M

M

M

M

F

F

uy

yy

ux

xx

cl

c

14

STEPS IN BEAM-COLUMN ANALYSIS

Steps in Beam-Column Analysis Calculate section properties Evaluate the type of section Check using interaction equation for section

yielding Check using interction equation for overall

buckling

15

SUMMARY

Short Beam-Columns Fail by Section Plastification

Slender Beam-Columns may Fail By Section Plstification Overall Flexural Yielding Overall Torsional-Flexural Buckling

Intetaction Eqs. Conservatively Consider P- and P- Effects

Advanced Analysis Methods Account for P- and P- Effects, directly & more accuraely