design of hrs - axial members

Design of Steel Structures

Design of Axial Members

Naveed Anwar, Buddhi Sharma

ACECOMS, AIT

Co-sponsored by:

Siam Yamato Steel Co., Ltd.

ACECOMS: Design of Steel Structures -

Axial Members: Strut-Tie

Tension Members

Compression Members

Axial Members


Cross-section Shapes

• Shapes used for this Seminar and SYSSoftware

– Wide Flange, W = H

– Narrow Flange, S, M = I

– Tees, WT, TH = T

– Angles

• Equal Angle Single: L, EL

• Unequal Angle Single : UL

• Double Angle : ELL, ULLS, ULLL

– Built-up Channels

• Back to Back: CCI

• Box : CCB


Tension Members

• Common Usage

– Tie Rods, Sag Rods

– Tension Members in Trusses

– Tension Members in Bracing

• Critical Considerations

– Tensile stresses

– Effective Area

– Yield Strength, Fy

– Ultimate Strength, Fu

– Connections

Tension Members


Basic Governing Equations

gyt AFP 6.0

eut AFP 5.0

Smaller of the following Capacities

Pt = Capacity in Tension

Fy = Yield strength of steel

Fu = Ultimate strength of steel

Ag = Gross cross-section area

Ae = Effective area in tension

An = Net cross-section area

U = Area reduction factor

x = Distance between centroid

and shear plane of connection

L = Length of connection

ne AUA

L

xU

1

Where


Overall Design Process

Pt, Fy,, Fu , L Compute Ag1 Determine U

Compute Ae

Compute Ag2

Accept Section

Design OK

Select

Section

Determine K

Kl/r < 300

Compute KL/r

max2

1

g

g

g A

AA

U

AA e

g 2

y

tg

F

PA

6.01

u

te

F

PA

5.0

Tension Members

Apply Net Area

Correction



1. Compute Ag1 based on Yield Criteria (Fy)

2. Compute Ae based on Fracture Criteria (Fu)

3. Select Area Reduction Factor, U

Based on connection type etc ( U = 0.75 - 1.0)

4. Compute Ag2 based on Ae from step 3

5. Select section to satisfy higher of Ag1 and Ag2

6. Check for other end connection requirements

Tension Members


Net Effective Area, Ae

• Why Net Effective Area?

To account for efficiency of end connections

Shear lag effect caused by partial connection and

uneven stress distribution

Many other factors that affect connection strength

• How to Calculate?

Tension Members

For Bolted and Riveted Connections, Ae = U An

For Welded Connections, Ae = U Ag

AgAnAg = Gross Area

An = Net area after holes

Ae = Effective Area


General Effective Area Factor, U

L

X X

X

X

connectiontheofLengthL

planesheartheandAreaconnectedthe

ofCentroidBetweenceDisx

L

xU

tan

1

X


WF Bf/ d>2/3

Ae

=0.75 An

Single or Double

Angle

Ae

=0.85 An

WT Bf/ d>2/3

Ae=0.90A

n

WF Bf/ d<2/3

Ae=0.85A

n

WF Bf/ d<2/3

Ae=0.75A

n

Single or Double

Angle

Ae

=0.75 An

Bar or Plate

Ae =An

WF Bf/ d>2/3

Ae=0.9A

n

Effective Area Factor, U

Tension Members

Typical Values of U for various cases


Area Reduction Factors

Special Cases for Welded Connections

A - For any H, I, T connected by transverse welds alone

U = 1.0, Ae = area of connected element

B - For plates and bars connected by longitudinal welds

alone, values of U depending upon the relative length of

the weld and their spacing

U=1.0 for l >= 2w

U=0.87 for 1.5 =< l < 2w

U=1.0 for w =< l < 1.5w

Tension Members

w

L

Only Transverse Weld

w

L

Only Logtudinal Weld


Axial Members: Strut-Tie

Tension Members

Compression Members

Axial Members


Compression Members

• Common Usage

– Struts

– Compression Members in Trusses

– Compression Members in Bracing

– Columns without significant Moment

• Critical Considerations

– Axial Stresses

– Axial- Flexural Buckling

– Flexural-Torsional Buckling

– Local Buckling

– Effective Length, kL and Slenderness Ratio, kL/r

Compression Members


Compression: Influencing Factors

– Grade of Steel

Stress-strain relations

Yield stress

– Manufacturing method - Residual Stresses

Hot rolled shape

Welded buil-up shape

Using flame-cut plates

Using universal mill plates

Cold-straightened shape

Rotorizing ( continuous straightening )

Gag ( point ) straightening

Compression Members


Compression: Influencing Factors

– Size and Properties of section ( Ag, rx, ry )

– Cross section geometry ( W, H, C,WT etc )

– Bending axis (Major or minor)

– Initial out-of-straightness

Maximum value

Distribution along column length

– Framing and End support conditions

Without sway, pinned or otherwise

With sway, pinned or otherwise

Restrained ends, with or without sway

Unsupported Member Length

Compression Members


Basic Strength Equation

'

asaa FQQF

aF

aQ

sQ

= Permissible stress as determined by bend buckling

criteria (based on basic equations without Qa ad Qs)

= Effective area correction factor

= Stress reduction factor based on width-thickness ratio

ga AFP P = Axial Capacity of Member

Fa = Permissible stress

Ag = Gross cross-section Area

Compression Members



gasa AFQQP'

Compression Members

Permissible stress as determined

by bend buckling criteria


Determination of Fa

For compression members, the critical (ultimate) stress,

including the effect of Residual Stresses, Initial Imperfections

and other non-linear factors is given by the general equation:

2

/

2

11

c

ycrC

rkLFF

c

v

ccr

a

Cr

kLfor

r

kLfor

FOS

F

EC

FOS

FF

92.1

067.1

2,

'

For AISC/ASD


Determination of Fa’

Fy

ECc

2

3

2

'

/

8

1/

8

3

3

5

/

2

11

cc

c

y

a

C

rKL

C

rKL

C

rKLF

F

Compression Members

2

2'

23

12

r

KL

EFa

r

KLCact .max

Cact >= Cc

Slender

Y

• Takes into account Section

Size, Length, End

Conditions etc.

• Main Problem is the

Effective Length Factor “K”


Effective Length Factor, K

• To account for “Axial-Flexural Buckling”

• Indicates the “total bent” length of column between

inflection points

• Can vary from 0.5 to Infinity

• Most common range 0.75 to 2.0

0.5 1.02.0

0.5 - 1.0 1.0 -

Compression Members


K Factor Examples

Model Example Factor

1.0

0.85

0.7

2.0

1.0

Compression Members


Determination of K

• Isolated Members

Fix Pin Free

Fix 0.5 0.8 2.0

Pin 0.8 1.0 Unstable

Free 2.0 Unstable UnstableBott

om

En

d

Top End

Compression Members


Determination of K

• Members Part of Framed Structure

IncreasesKIncreaseGGK

BeamsLEI

ColumnsLEIG C

,

)/(

)/(

2120

20

mm

m GforGG

K

2)1(9.0 mm GforGK

0.105.085.0

0.1)(05.07.0

m

BT

Gk

GGK

Unbraced

Frames

Braced

Frames

(smaller of)

BTm

B

T

GandGofMinimumG

EndBottomG

EndTopG

Compression Members



Compression Members

gasa AFQQP'

Stress reduction factor based on width-thickness ratio

To account for Local Buckling of Un-Stiffened Plates


• Accounts for “Local Plate Buckling”

• Governed by “Thinnest” (max b/t)

Un-stiffened element

Stress Reduction Factor, Qs

K = Factor based plate boundary

E = Modulus of Elasticity

b = Width of plate

t = Thickness of plate

m = Poison Ratio = 0.3

2

2

2

112

t

b

EKPcr

m

2/

9.0,

tb

KEPor cr

The codes use various limits on (b/t ) to specify some empirical

values of stress reduction factor in terms of Fy to take into

account post-buckling strength of un-stiffened elements

Compression Members


Stress Reduction Factor, Qs

y

yy

y

s

Ffor

FFforF

Q155

t

b

(b/t)F

15,500

155

t

b76

t

b 00447.0340.1

2

y

y

yy

y

s

Ffor

FFforF

Q195

t

b

(b/t)F

20,000

195

t

b95

t

b 00437.0415.1

2

y

y

yy

y

s

Ffor

FFforF

Q176

t

b

(b/t)F

20,000

176

t

b127

t

b 00715.0908.1

2

y

For stems of tees

For projecting

elements of

compression flanges

of columns and beams

For single angles

Compression Members


Qa for Fy = 2400 Ksc (34 ksi)

3.26t

b

(b/t)

446.7

3.26t

b9.12

t

b 026.0340.1

2for

for

Qs

1.33t

b

(b/t)

576.4

1.33t

b1.16

t

b 0257.415.1

2for

for

Qs

9.29t

b

(b/t)

576.4

9.29t

b6.21

t

b 0421.0908.1

2for

for

QsFor stems of tees

For projecting

elements of

compression flanges

of columns and beams

For single angles

Compression Members



Compression Members

gasa AFQQP'

Effective area correction factor to

account for Non-Linear Stress Distribution on Stiffened Elements


Effective Area Factor, Qa

• To account for “Non-uniform, Non-linear, Post-buckling

Stress Distribution” or “Karman” effect

• Governed by “Thinnest” (max. b/t) stiffened element

• Effective Area, Ae

– for “Un-stiffened” elements of the section, be = b

– for “Stiffened” elements, be must be computed

g

ea

A

A

AreaGross

AreaEffectiveQ

Compression Members

tbA ee



Compression Members

Non-linear Compressive Stress

Distribution in Stiffened Elements

Stiffened

Element

Un-Stiffened

Element

be = 1

be/2


Effective Plate Width, be

Compression Members

bftbf

tbe

)/(

9.641

326

bftbf

tbe

)/(

2.571

326

For flanges of rectangular box sections

Other uniformly compressed stiffened elements

f = P/Ag for columns (in ksi)

f = M/Sx for beams (approx.) (in ksi)



• Example:

Compression Members

b e2

2

b e2

2

b2 t2

t1

b1

2211

2211

2

2

tbtb

tbtbQ e

a


Design Steps

1. Assume a trial section by judgement and experience or by

using design aids

2. Assume Qa=1.0 for first trial

3. Compute Qs based on the specification formula

4. Compute the critical slenderness ratio Cc

5. Assume or compute the Kx and Ky by using alignment chart

or equations.

6. Compute Cact , the highest KL/r

7. Compute Fa based on Cc and Cact

Compression Members


Design Steps

8. Revise the value for Qa by using new value for Fa .

If the new Qa is same as assumed then accept Fa (Go to

next step) otherwise revise the Fa ( Go back to step 4 ).

Repeat the procedure until the desired accuracy is obtained.

9. Compute the capacity based on gross area and the Fa

computed from step 8

10. If the section capacity is more than or equal to the required

capacity accept the section otherwise try new section and

repeat the whole calculation until suitable section is found

Compression Members


Compute Fa


P, W, Fy, LSelect

SectionDetermine K

Assume Qa,

Compute Qs

Compute Cc

Compute Cact

Compute Fa

Compute Qa2Qa2 ~ QaCompute Pn

Pn > PAccept Section

Design OKQa2= Qa

Compression Members


The Stress Ratio Components

0.1 bybxa RRRR

a

aa

F

fR

'

asaa

g

a

FQQF

A

Pf


Unsymmetrical Sections

• Special Considerations for

• Angle, Double Angle, Tee, Zee etc

• Covered by special methods and specifications

Compression Members

ACECOMS: Design of Steel Structures - Compression Members

design of hrs - axial members

Documents

siam yamato steel

area reduction factorx

area of connected elementb

connection strength

trusses tension members

compute ag1

sag rods tension members

effective areaacecoms