1. IS 800 : 2007 GENERAL CONSTRUCTION IN STEEL – CODE OF PRACTICE (Third Revision)

2. DESIGN OF TENSION MEMBERS

3. (b) Suspended Building
INTRODUCTION
tie
(a) Roof Truss
rafter
(b) Suspended Building
(b) Roof Purlin System
purlin
Sag rod
Top chord
(c) Braced frame
Tension Members in Buildings

4. Characteristics
Members Experience
Axial force
Stretching
Uniform stress over the cross section
Very Efficient Member
Strength governed by the material strength
Bolt holes affect the strength

5. Cross Sections Used for Tension Members
Channel
Angle
Double Angle
Rod
Cable
Built up sections

6. IS 800 – 1984 IS

7. SECTION 6 DESIGN OF TENSION MEMBERS
6.2 Design Strength due to Yielding of Gross Section
6.3 Design Strength due to Rupture of Critical Section
6.3.1 Plates
Threaded Rods
Single Angles
6.3.4 Other Sections
6.4 Design Strength due to Block Shear

8. CODAL PROVISIONS 6.1 Tension Members
The factored design tension T, in the members T < Td
6.2 Design Strength due to Yielding of Gross Section
The design strength of members under axial tension Tdg, Tdg = fy Ag /m0
6.3 Design Strength due to Rupture of Critical Section
6.3.1 Plates  The design strength in tension of a plate, Tdn,
Tdn =0.9 fu An / m1
Cont…

9. BEHAVIOUR IN TENSION Material Properties T fy c  High Strength Steel
Mild Steel
High Strength Steel T  a b c d e fy
0.2%
Yield Plateau

10. BEHAVIOUR IN TENSION Plate with a Hole (a) Elastic (b) Elasto-Plastic
(c) Ultimate u y
Plate with a Hole

11. BEHAVIOUR IN TENSION Plates with Holes (a) (b) (c) P = pitch g = gauge1 4 p g 2 3 b d
Case a: Net Area: = t (b - 2*d)
Case b: Net Area: = t (b – d)
Case c: Net Area: < t (b – d)
> t (b - 2*d)
Plates with Holes
(a)
(b)
(c)

12. BEHAVIOUR IN TENSION
Plates with Holes
An = [ b – n d + (p2 / 4 g)] t

13. The design strength of threaded rods in tension, Tdn,
Tdn =0.9 fu An / m1
Ultimate
elastic
elastic -Plastic
droot
dgross
f < fy fy fu

14. BEHAVIOUR OF ANGLES UNDER TENSION
ANGLES Eccentrically Loaded Through Gussets
Gusset plate

15. ANGLES UNDER TENSION Factors Affecting Angle Strength
Effect of Gusset Thickness
Effect of Angle Thickness
Effect of Shear Lag
Effect of End Connections
Effect of Block Shear

16. ANGLES UNDER TENSION Effect of Shear Lag Shear Lag Strength Reduction
Shear Lag as Ao / Ag
Shear Lag as end connection Stiffness

17. 6.3.3 Single Angles  The design strength, Tdn, as governed by tearing
CODAL PROVISIONS
6.3.3 Single Angles  The design strength, Tdn, as governed by tearing
Tdn = 0.9 fu Anc / m1 + Ago fy /m0
 = 1.4 – (w/t) (fu/fy) (bs/L ) ≈ (bs/L)
Alternatively, the tearing strength of net section may be taken as
Tdn =  An fu /m

18. Fig. 6.1 Angles with end connections
bs=w w w1
bs=w+w1
Fig. 6.1 Angles with end connections

19. Tdb = ( Avg fy /(3 m0) + fu Atn /m1 ) or
CODAL PROVISIONS
6.4 Design Strength due to Block Shear
6.4.1 Plates –The block shear strength, Tdb, of connection shall be taken as the smaller of
Tdb = ( Avg fy /(3 m0) + fu Atn /m1 ) or
Tdb = ( fu Avn /(3 m1) + fy Atg /m0 ) 1 2 3
Fig 6.3 Block Shear Failure of Angles 4
Fig 6.2 Block Shear Failure of Plates 1 2 4 3

20. DESIGN OF TENSION MEMBERS
Efficiency
= Pt /(Ag * fy / M0)
Design Steps
An = Pt / (fu / M1)
Ag = Pt / (fy / M0)
Choose a trial section with the design strength greater than or equal to the maximum factored design tension load.

21. DESIGN OF COMPRESSION MEMBERS

22. INTRODUCTION
Dominant factors affecting ultimate strength of columns subjected to axial compressive loading:
Slenderness ratio (/r)
Material yield stress (fy)
Dominant factors affecting ultimate strength of practical columns:
Initial imperfection
Eccentricity of loading
Residual stresses
Strain hardening

23. DESIGN STRENGTH OF COMPRESSION MEMBERS
Old Code
The axial stress in compression is given by
Where
fy = yield stress of steel;
fcc = Elastic critical stress in compression
E = Modulus of elasticity.
 (= L/r) = slenderness ratio of the member
n = a factor assumed as 1.4
L/r = ratio of effective length to appropriate radius of gyration. ( ) 1 y f cr [ ] n y f
fcc σ + =

24. Typical column design curve
INTRODUCTION c fy
Test data (x) from collapse tests
on practical columns
Euler curve
Design curve
Slenderness  (/r) x
x x
x x x
x x
200
100
Typical column design curve

25. Cross Section Shapes for Rolled Steel Compression Members
(a) Single Angle
(b) Double Angle
(c) Tee
(d) Channel
(e) Hollow Circular
Section (CHS)
(f) Rectangular Hollow
Section (RHS)

26. (f) Built-up Box Section
Cross Section Shapes for Built - up or
fabricated Compression Members
(b) Box Section
(c) Box Section
(d) Plated I Section
(e) Built - up I Section
(f) Built-up Box Section
(a) Box Section

27. SECTION 7 DESIGN OF COMPRESSION MEMBERS
7.1 Design Strength
7.2 Effective Length of Compression Members
7.3 Design Details
7.4 Column Bases
7.5 Angle Struts
7.6 Laced Columns
7.7 Battened Columns
7.8 Compression Members Composed of Two Components Back-to-Back

28. 7.1 DESIGN STRENGTH
The design compressive strength of a member is given by
 = 0.5[1+ ( - 0.2)+ 2]
fcd = the design compressive stress,
λ = non-dimensional effective slenderness ratio,
fcc = Euler buckling stress = 2E/(KL/r)2
= imperfection factor as in Table 7.1
 = stress reduction factor as in Table 7.3

29. 7.1.2.1 The classification of different sections under different buckling class
a, b, c or d, is given below.
Cross Section
Limits
Buckling about axis
Buckling Curve
Rolled I-Sections
h/b > 1.2 : tf 40 mm
 40 < tf <100
z-z
y-y a b  b c
Welded I-Section
tf <40 mm
tf >40 mm
 z-z  c d
Hollow Section
Hot rolled
Cold formed
Any
Welded Box Section, built-up
Generally
Channel, Angle, T and Solid Sections

30. 7.1 DESIGN STRENGTH a b c d

31. Schematic representation
7.2 Effective Length of Compression Members
Boundary Conditions
Schematic representation
Effective Length
At one end
At the other end
Translation
Rotation
Restrained
Free
2.0L
1.0L
1.2L
0.8L
0.65 L

32. 7.4 COLUMN BASES

33. DESIGN CONSIDERATIONS FOR LACED AND BATTENED COLUMNS
(a) Single Lacing
(b) Double Lacing
(c) Battens
Built-up column members

34. LACED AND BATTENED COLUMNS
The effective slenderness ratio, (KL/r)e = 1.05 (KL/r)0,
to account for shear deformation effects.
The effective slenderness ratio of battened column, shall be taken as 1.1 times the (KL/r)0, where (KL/r)0 is the maximum actual slenderness ratio of the column, to account for shear deformation effects.

35. STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS
Design steps:
Assume a suitable trial section.
Arrive at the effective length of the column.
Calculate the slenderness ratios.

36. STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS
Calculate e values along both major and minor axes.
Calculate  = [( - 0)],
Calculate  and c .
Compute the load that the compression member can resist (c A).

37. Resistance of Cross-section
For members connected by welding,
design tension resistance Nt.Rd is
A is the gross area of the cross-section
For members connected by bolting,
design tension resistance Nt.Rd is reduced due to presence of holes and is the lesser of
0,9 is a reduction factor for eccentricity, stress concentration etc
Anet is the net area of the cross-section
fu is the ultimate tensile strength or

38. Characteristics
Members Experience
Axial force
Stretching
Uniform stress over the cross section
Very Efficient Member
Strength governed by the material strength
Bolt holes affect the strength

39. BEHAVIOUR IN TENSION Plate with a Hole (a) Elastic (b) Elasto-Plastic
(c) Ultimate u y
Plate with a Hole

41. ANGLES UNDER TENSION Factors Affecting Angle Strength
Effect of Gusset Thickness
Effect of Angle Thickness
Effect of Shear Lag
Effect of End Connections
Effect of Block Shear

44. Introduction
This lecture is concerned with compression members (eg pin-ended struts) subject to
axial compression only
no bending
In practice real columns are subject to
eccentricities of axial loads
transverse forces
The treatment distinguishes between
stocky columns, and
slender columns

46. Stocky columns The characteristics of stocky columns are
very low slenderness
unaffected by overall buckling
The compressive strength of stocky columns is
dictated by the cross-section
a function of the section classification

47. Cross-sections not prone to local buckling
Class 1, 2, 3 cross-sections are unaffected by local buckling
design compression resistance Nc.Rd equals the plastic resistance Npl.Rd
Nc.Rd = Afy /gM (1) a)

48. Cross-sections prone to local buckling - Class 4
local buckling prevents the attainment of the squash load
design compression resistance limited to local buckling resistance,
Nc.Rd = No.Rd = Aefffy /gM (1) b)
Aeff is the area of the effective cross-section

49. Behaviour of real steel columns
inelastic buckling occurs before the Euler buckling load due to various imperfections
initial out-of-straightness
residual stresses
eccentricity of axial applied loads
strain-hardening
columns of medium slenderness are very sensitive to the effects of imperfections

50. DESIGN PHILOSOPHY Ptg = fy * Ag /MO MO = 1.10
Gross Area Design Strength (Ptg)
Ptg = fy * Ag /MO MO = 1.10
Net Area Design Strength (Ptn)
Ptn = 0.9 * fu * An / M1 M1 = 1.25

51. INFLUENCE OF RESIDUAL STRESSES
Rolled beam C
Welded box T
Rolled column
Distribution of residual stresses
Heavily welded section:
Residual stresses due to welding are very high and can be of greater consequence in reducing the ultimate capacity of compression members.

52. BEHAVIOUR OF ANGLE COMPRESSION MEMBERS
Angles under compression
Concentric loading - Axial force
1. Local buckling
2. Flexural buckling about v-v axis
3. Torsional - Flexural buckling about u-u axis
Eccentric loading - Axial force & bi-axial moments
Most practical case
May fail by bi-axial bending or FTB
(Equal 1, 2, 3 & Unequal 1, 3) V U

53. Complexity in analysis and design
Axial compression &
bi-axial bending
Eccentric Loading
Effect of end restraint
Principal axes do not coincide with geometric axis
Type of Connection
One bolt
Multiple bolt
Weld
Rotational restraint
provided by gusset

54. PARAMETERS TO BE CONSIDERED
FAILURE
Flexural torsional buckling
PARAMETERS TO BE CONSIDERED
Primary parameters
L/r ratio
b/t ratio
Type of connection
Secondary parameters
Effect of connection length
Effect of gusset thickness
Weld or 2B or multiple bolted
Single bolted

55. CURRENT DESIGN PRACTICE
Two approaches
Treat the angle as an equivalent concentrically loaded column
Modifying effective length
Reducing axial capacity
Treat angle as a pin ended beam-column

56. COMPARISON OF TENSION MEMBERS

57. DESIGN STRENGTH OF TENSION MEMBERS
Old Code
It takes a certain percentage of the outstanding leg area to be effective in determining the tensile strength as given below:
Td = [Anc + K Ao] Fy

58. IS 800 – 1984 IS

59. DESIGN STRENGTH DUE TO YIELDING OF GROSS SECTION
New Code
The design strength of members under axial tension Tdg, as governed by yielding of gross section, is given by
Tdg = fy Ag /m0
where
fy = yield strength of the material in MPa
Ag = gross area of cross section in mm2
m0 = partial safety factor for failure in tension by yielding

60. DESIGN STRENGTH DUE TO RUPTURE OF CRITICAL SECTION
New Code
Plates  The design strength in tension of a plate, Tdn, as governed by rupture of net cross sectional area, An, at the holes is given by
Tdn =0.9 fu An / m1
where
m1 = partial safety factor
fu = ultimate stress of the material in MPa
An = net effective area of the member, =
Threaded Rods  The design strength of threaded rods in tension, Tdn,

61. DESIGN STRENGTH DUE TO RUPTURE OF CRITICAL SECTION (Contd..)
Single Angles  The design strength, Tdn, as governed by tearing
Tdn = 0.9 fu Anc / m1 + Ago fy /m0
 = 1.4 – (w/t) (fu/fy) (bs/L ) ≈ (bs/L)
Alternatively, the tearing strength of net section may be taken as
Tdn =  An fu /m1

62. Angles with end connections
bs=w+w1
bs=w
Design Strength due to Block Shear
Plates –The block shear strength, Tdb, of connection shall be taken as the
smaller of
Tdb = ( Avg fy /(m0) + fu Atn /m1 ) or
Tdb = ( fu Avn /(m1) + fy Atg /m0 )

63. COMPARISON OF COMPRESSION MEMBERS

64. DESIGN STRENGTH OF COMPRESSION MEMBERS
Old Code
The axial stress in compression, Fcr, is given by
Where
Fy = yield stress of steel;
Fe = Elastic critical stress in compression
E = Modulus of elasticity.
 (= L/r) = slenderness ratio of the member
n = a factor assumed as 1.4
L/r = ratio of effective length to appropriate radius of gyration.

65. DESIGN STRENGTH OF COMPRESSION MEMBERS
New Code
The design compressive strength of a member is given by Pd = Ae fcd
The design compressive stress, fcd, of axially loaded compression members
λ = non-dimensional effective slenderness ratio, ,
fcc = euler buckling stress = 2E/(KL/r)2
 = 0.5[1+ ( - 0.2)+ 2]

66. The classification of different sections under different buckling class a, b, c or d, is given below. a b c d

67. COMPARISON OF OLD CODE TO NEW CODE

68. ECCENTRICALLY LOADED SINGLE ANGLE COMPRESSION MEMBERSV U
Angles under compression
Concentric loading - Axial force
1. Local buckling
2. Flexural buckling about v-v axis
3. Torsional - Flexural buckling about u-u axis
Eccentric loading - Axial force & bi-axial moments
Most practical case
May fail by bi-axial bending or FTB
(Equal 1, 2, 3 & Unequal 1, 3) V U

69. Old Code Two approaches
Treat the angle as an equivalent concentrically loaded column
Modifying effective length
Reducing axial capacity
Treat angle as a pin ended beam-column

70. DESIGN OF TENSION MEMBERS
Stiffness Requirements
Designed for compression under
stress reversal /r < 250
Not designed for compression under
stress reversal /r < 350
Members under tension only /r < 400

71. Euler buckling curve and modes of failure
Failure by yielding s fy
Failure by buckling
Euler buckling curve l l1

72. two regions: slender (beyond point of inflexion) & medium
Experimental studies
two regions: slender (beyond point of inflexion) & medium s
Medium slenderness
Large slenderness fy
Point of inflexion l1 l

73. Effect of imperfections in relation to slenderness
Columns of large slenderness
largely unaffected by imperfections
ultimate failure load  Euler load independent of the yield stress
Columns of medium slenderness
imperfections important
failure load less than Euler load
out-of-straightness and residual stresses are the most significant imperfections

74. Residual stresses patterns
Typical residual stress pattern ~ , 3 f y
compression ~ , 2 f y
tension ~ , 2 f y
compression
due to hot rolling

75. Combination with axial stresses
Residual stresses
combined with axial stresses cause yielding
effective area reduced + = o r = f N / A s s y R n
< f y s n
reaching f y
Combination with axial stresses

76. Initial out-of-straightness eo
induces bending moments N e o e s B N

77. Initial out-of-straightness eo
If smax > fy the section becomes partly plastic P
Yielded
zones P

78. Combined effect of imperfections and axial load
maximum stress - combination of
bending stress sB
residual stress, sR
applied axial stress, N/A s s s N / A R B m a x + + =

79. buckling curves
column strength is defined by a reduction factor  applied to the yield strength fy
 is related to the reference slenderness
buckling curves plotted as  versus reference slenderness ratio

80. Assumptions Based on a half sine-wave geometric imperfection = L/1000
residual stresses related to section type
4 curves apply to different cross-section types corresponding to different values of the imperfection factor a

81. buckling curves The curves can be expressed mathematically as:
(1) (5.46)

82. Design Steps (2) select appropriate buckling curve taking into account
the forming process
the shape thickness
determine  for the value of

83. SECTION 7 DESIGN OF COMPRESSION MEMBERS
7.1 Design Strength
7.2 Effective Length of Compression Members
7.3 Design Details
7.4 Column Bases
7.5 Angle Struts
7.6 Laced Columns
7.7 Battened Columns
7.8 Compression Members Composed of Two Components Back-to-Back

84. Typical column design curve
INTRODUCTION c fy
Test data (x) from collapse tests
on practical columns
Euler curve
Design curve
Slenderness  (/r) x
x x
x x x
x x
200
100
Typical column design curve

85. Effective cross-sections
The centroidal axis of the effective cross-section may shift relative to that for the gross cross-section.
For a member subject to an axial force, the shift of the centroidal axis will give rise to a moment which should be accounted for in member design.

86. Effective cross-sections
For a member in bending, shift of the centroidal axis of the effective cross-section relative to that for the gross cross-section. will be taken into account when calculating the section properties of the effective section.

87. 7.4 COLUMN BASES

88. DESIGN CONSIDERATIONS FOR LACED AND BATTENED COLUMNS
(a) Single Lacing
(b) Double Lacing
(c) Battens
Built-up column members

89. LACED AND BATTENED COLUMNS
The effective slenderness ratio, (KL/r)e = 1.05 (KL/r)0,
to account for shear deformation effects.
The effective slenderness ratio of battened column, shall be taken as 1.1 times the (KL/r)0, where (KL/r)0 is the maximum actual slenderness ratio of the column, to account for shear deformation effects.

90. STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS
Design steps:
Assume a suitable trial section.
Arrive at the effective length of the column.
Calculate the slenderness ratios.

91. STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS

92. DESIGN OF TENSION MEMBERS
Efficiency
= Pt /(Ag * fy / M0)
Design Steps
An = Pt / (fu / M1)
Ag = Pt / (fy / M0)
Choose a trial section with the design strength greater than or equal to the maximum factored design tension load.

93. Topics 1. Introduction 2. Static Analysis Dynamic Analysis
Stochastic Dynamic Analysis of RC Chimneys

94. Topics