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

DESIGN OF TENSION MEMBERS

(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

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

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

IS 800 – 1984 IS 800 - 2007

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 6.3.2 Threaded Rods 6.3.3 Single Angles 6.3.4 Other Sections 6.4 Design Strength due to Block Shear

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…

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

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

BEHAVIOUR IN TENSION Plates with Holes (a) (b) (c) P = pitch g = gauge 1 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)

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

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

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

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

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

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 – 0.035 (w/t) (fu/fy) (bs/L ) ≈ 1.4-0.52(bs/L) Alternatively, the tearing strength of net section may be taken as Tdn =  An fu /m

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

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

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.

DESIGN OF COMPRESSION MEMBERS

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

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 + ´ =

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 50 100 150 Typical column design curve

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)

(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

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

7.1 DESIGN STRENGTH 7.1.2 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

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

7.1 DESIGN STRENGTH a b c d

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

7.4 COLUMN BASES

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

LACED AND BATTENED COLUMNS 7.6.1.5 The effective slenderness ratio, (KL/r)e = 1.05 (KL/r)0, to account for shear deformation effects. 7.7.1.4 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.

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.

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).

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

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

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

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

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

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

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 /gM0 5.4.4(1) a)

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 /gM1 5.4.4.(1) b) Aeff is the area of the effective cross-section 5.3.5

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

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

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.

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

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

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

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

COMPARISON OF TENSION MEMBERS

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

IS 800 – 1984 IS 800 - 2007

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

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,

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 – 0.035 (w/t) (fu/fy) (bs/L ) ≈ 1.4-0.52(bs/L) Alternatively, the tearing strength of net section may be taken as Tdn =  An fu /m1

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 )

COMPARISON OF COMPRESSION MEMBERS

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.

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]

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

COMPARISON OF OLD CODE TO NEW CODE

ECCENTRICALLY LOADED SINGLE ANGLE COMPRESSION MEMBERS V 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

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

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

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

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

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

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

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

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

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

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 + + =

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

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

buckling curves The curves can be expressed mathematically as: 5.5.1.2.(1) (5.46)

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

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

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 50 100 150 Typical column design curve

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.

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.

7.4 COLUMN BASES

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

LACED AND BATTENED COLUMNS 7.6.1.5 The effective slenderness ratio, (KL/r)e = 1.05 (KL/r)0, to account for shear deformation effects. 7.7.1.4 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.

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.

STEPS IN THE DESIGN OF AXIALLY LOADED COLUMNS

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.

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

Topics