Design provisions of BS 5950 part‐1
Prepared : Ismael .S Lead : Tridibesh Indu Project : SOGT Malaysia SAMSUNG ENGINEERING INDIA
Contents Introduction General
Scope, References & Definitions
Limit state design
General principles and design methods Ultimate limit states Serviceability limit states
Properties of materials & Section Properties
Structural steel Bolts and welds
Design of structural members
Tension members Compression members Members subjected to bending Combined moment and axial force
Continuous structures Connections Loading Tests
Introduction
Objective : To study and present the provisions of BS 5950 part‐1 related to the design of tension members, compression members and flexural members
Scope : The BS 5950 Part‐1 gives recommendations for the design of structural steelwork using Hot rolled steel sections, Flats, Plates, Hot finished structural hollow sections, Cold formed structural hollow sections in buildings and allied structures.
Limit state design General principle : The aim of structural design should be to provide, a structure capable fulfilling its intended function and sustaining the specified loads for its intended life with due regard to economy . Appropriate partial factors should be applied to provide adequate degrees of reliability for ultimate limit states and serviceability limit states. 1. Ultimate limit states
concerning the safety of the whole or part of the structure.
In checking the strength of a structure, or of any part of it, the factored loads should be applied in the most unfavorable realistic combination for the part or effect under consideration The load carrying capacity of each member and connection, should be such that the factored loads would not cause failure.
Limit state design Load combinations (ULS): Load combinations 1 2
3
Dead & Imposed loads (gravity loads)
1.4 DL
Dead load & Wind (WL) or Earthquake load (EL)
1.0 DL+1.4 WL
Dead load, Imposed load & WL or EL
1.4 DL + 1.6 LL 1.4 DL+1.4 WL 1.4 DL+1.4 EL 1.2 DL+1.2 LL+1.2 WL
In comb 1, the Notional horizontal force should be applied, taken as a min of 0.5 % of the factored vertical dead and imposed loads In comb 2 & 3, the horizontal component of the factored wind load should not be taken as less than 1.0% of the factored dead load applied horizontally
1.2 DL+1.2 LL+1.2 EL
As the specified loads from overhead travelling cranes already include significant horizontal loads, it is not necessary to include vertical crane loads when calculating the minimum wind load / notional horizontal forces.
Limit state design 2. Serviceability limit states
correspond to limits beyond which specified service criteria are no longer met.
‐Deflection ‐Vibration and Oscillation ‐Durability Load combinations 1 2
3
Dead & Imposed loads (gravity loads)
1.0 DL
Dead load & Wind (WL) or Earthquake load (EL)
1.0 DL+1.0 WL
Dead load, Imposed load & WL or EL
1.0 DL + 1.0 LL 1.0 DL+1.0 EL 1.0 DL+ 1.0 LL+ 0.8 WL 1.0 DL+ 1.0 LL+ 0.8 EL
Exceptional snow loads should not be included in the imposed load when checking serviceability. In case of combined LL & WL, only 80% of the full specified value need be considered when checking serviceability
Limit state design Stability Limit State ‐Static equilibrium
Sliding, Overturning or Lift off its seating.
‐Resistance to Horizontal Force
Notional Horizontal force & WL etc.
Notional horizontal force To allow for the effects of practical imperfections such as lack of verticality, all structures should be capable of resisting notional horizontal forces, taken as a minimum of 0.5 % of the factored vertical dead and imposed loads applied at the same level. The notional horizontal forces should be assumed to act in any one direction at a time and should be applied at each roof and floor level or their equivalent. They should be taken as acting simultaneously with the factored vertical dead and imposed loads (load combination 1). The notional horizontal forces should not be applied −when considering overturning & pattern loads −with horizontal loads & temperature effects The notional horizontal forces should not be taken to contribute to the net reactions at the foundations.
Limit state design ‐ Sway stiffness All structures should have sufficient sway stiffness, so that the vertical loads acting with the lateral displacements of the structure do not induce excessive secondary forces or moments in the members or connections. Non‐sway: If the sway mode elastic critical load factor under vertical load Where,
λcr > 10
λcr = h / 200 δ h ‐ is storey height δ ‐ is deflection of top of storey relative to bottom of storey due to notional horizontal force
Sway‐sensitive: Secondary forces and moments should be allowed by multiplying the sway effects by the amplification factor “kamp”. Where, kamp = λcr/(1.15λcr‐1.5)
but kamp > 1.0
Properties of Material ‐ Structural Steel The design strength py for commonly used grades and thicknesses of steel is specified in BS 5950‐2, Alternatively from Table 9 of BS 5950‐1. The design strength py should be taken as 1.0Ys but not greater than Us /1.2 Ys ‐ the minimum yield strength Us ‐ the minimum tensile strength
Properties of Material ‐ Structural Bolts Strength of bolts (MPa) Bolt grade
Shear ps
Bearing pbb
Tension pt
4.6
160
460
240
8.8
375
1000
560
10.9
400
1300
700
< M24
400
1000
590
> M27
350
900
515
Higher grade HSFG to BS 4395‐‐2 400
1300
700
Other grades (Ub < 1000 MPa)
0.7 (Ub+Yb)
0.7Ub but< Yb
General grade HSFG to BS 4395
0.4 Ub
Ub is the specified minimum tensile strength of the bolt. Yb is the specified minimum yield strength of the bolt.
Section properties Net area :
an = ag – Deduction for bolt holes
Case 1. Bolt holes not staggered
an = ag – n (Dt)
Case 2. Staggered bolt holes, the net area is the smaller of Holes Staggered C
an = ag – n (Dt)+ (n‐1) (s2/4g)
Holes in line A
an = ag – n (Dt) Number of staggers
Where, ag ‐ gross area n ‐ number of holes D ‐ dia of hole t ‐ thickness of holed material Effective net area :
ae = Kean
ae < ag ae < 1.2 an
Effective net area coefficient for Steel grade S 275 : Ke = 1.2 Us – min tensile strength S 355 : Ke = 1.1 S 460 : Ke = 1.0 other : Ke = (Us/1.2)py
∑ae = Sum of effective net areas of all elements of the cross‐section
Yes
Connected to both sides of gusset & components are interconnected within their length.
z1
Mx < Mrx & My < Mry
My
Ft M x + + ≤1 Pt M cx M cy
z2
⎛M ⎞ ⎛ Mx ⎞ ⎟⎟ + ⎜⎜ x ⎟⎟ ≤ 1 ⎜⎜ ⎝ M rx ⎠ ⎝ M rx ⎠
Pt = py Ae tension capacity without considering eccentricity Mcx & Mcy are moment capacities (Ref. cl. 4.2.5)
welded bolted
Eccentric Connected ?
If doubly‐symmetric c/s
a2 = Ag – a1
Pt = py (Ae‐0.5a2)
Pt = py (Ag‐0.3a2)
a1 = Gross area of connected leg bolted
No
If plastic or compact section
welded
Pt = py ∑ae
Cl. 4.6.3.1
Pt = py Ae
Reduced tension Tension members capacity method with moments Cl. 4.6.3 Cl. 4.8.2
Mrx & Mry are reduced plastic moment capacities (Ref. cl. I2)
Cl. 4.6.3.2
Tension Capacity
Simplified method Exact method Cl. 4.8.2.2 Cl. 4.8.2.3
Design of Tension members
Pt = py (Ae‐0.25a2)
Pt = py (Ag‐0.15a2)
Classification of cross section Classification of cross sections helps to determine whether local buckling influences capacity, without calculating local buckling resistance. Supported edge Local buckling : buckling of the individual cross‐sectional elements x (webs, flanges, angle legs, etc.). b a Stability of these elements can be analyzed in
C
the context of thin plate theory. For a long rectangular thin plate subjected to edge compressive loading
2 2 ⎡ ⎛m⎞ ⎤ 2 ⎛a⎞ ⎛n⎞ N cr = π D⎜ ⎟ ⎢⎜ ⎟ + ⎜ ⎟ ⎥ ⎝ n ⎠ ⎣⎢⎝ a ⎠ ⎝ b ⎠ ⎦⎥ 2
Critical buckling load
Critical buckling stress pcr = N cr = π 2D k t bt (take m=1 & divide by 2 plate thickness ‘t’) kπ 2 E ⎛ t ⎞ 2
pcr =
Plate slenderness
(
b/t
Free edge
T
2
Here ‘n’ and ‘m’ represent the number of buckling waves in the x‐ and y‐directions.
)
(
py
y
⎜ ⎟ 12 1 −ν 2 ⎝ b ⎠
kπ 2 E ⎛b⎞ ⎜ ⎟= 12 1 −ν 2 pcr ⎝t⎠
pcr
(b/t)lim
Nx
)
Plate rigidity D =
Et 3 12 1 −ν 2
(
K ‐ Buckling coefficient
)
C
T
Classification of cross section Flange outstand element At py =275 MPa
k = 0.425 (b/t) =16.9
Flange internal element
k = 4
At py =275 MPa
(b/t) =51.9
Web element
k = 23.9
At design strength py =275 MPa
(b/t) =126.9
(Case ‐ E) (b/t) =15ε From table 11 (Case ‐ C) (b/t) =40ε From table 11
(b/t) =120ε From table 11
Slender (S): Cross‐sections which buckle before the stress at the extreme compression fibre reach design strength Semi‐compact (SC): Cross‐sections in which the stress at the extreme compression fibre can reach the design strength. Compact (C): Cross‐sections with plastic moment capacity. Plastic (P): Cross‐sections with plastic hinge rotation capacity.
Buckling coefficient ‘k’ For compression and bending
P Mp C My
M = py S
SC py Z < M < py S
S M = py Z M = py Zeff
Φ
Classification of cross section
Members subject to bending Structural members subjected to Flexure, either fail due to Yielding ‐ the cross section reaches full section capacity
Full lateral restraint provided
Full lateral restraint may be assumed to exist if the frictional or positive connection to the compression flange of the member is capable of resisting a lateral force > 2.5 % of the maximum force in it. To avoid irreversible deformation under serviceability loads, Mc < 1.5pyZ generally < 1.2pyZ in the case of a simply supported beam or a cantilever Lateral Torsional Buckling ‐ The compression flange of beam acts like a strut, being free to move in sideways it buckle dragging the reluctant tension flange behind, this results the twist of cross‐section. Distorted shape of one half of SS beam Web shear buckling If the ratio d/t exceeds 70ε for a rolled section, or 62ε for a welded section, the web should be checked for shear buckling.
Members subject to bending
Semi‐compact
:Mc = py Z
Slender
:Mc = py Zeff
Yes
Equivalent slenderness Limiting slenderness
Fv < 60%(Pv)
Mc = py (S – ρSv)
Mc = py (Z – ρSv/1.5) :Semi ‐ compact
Yes
No
If λLT < λL0 If λL0 < λLT<2λL0
Welded sections
If 2λL0 < λLT<3λL0 : ηLT = 2αLT(λL0)/1000 If λLT > 3λL0 : ηLT = αLT(λLT ‐ λL0)/1000
Elastic critical stress
LTB Resistance moment (Mb)
β = 1.0 for plastic & compact = Zx/Sx for semi compact = Zxeff / Sx for slender
: ηLT = 0 : ηLT = 2αLT(λLT‐λL0)/1000
pE = π2E/λLT2
ρ= [2(Fv/Pv) – 1]2
λ = kL / r v = 1/[1+0.05(λ/x)2]0.25 x = D / T u = 0.9 for rolled I,H or C = 1.0 for welded girder
Mb = Mc
Rolled sections
‘Sv’ is the plastic modulus of the shear area ‘Av’
Shear capacity Pv = 0.6pyAv
Mc = py (Zeff – ρSv/1.5) :Slender
λL0 = 0.4(π2E/py)0.5
Perry factor
Bending strength
:Plastic & compact
λLT = u v λ (β)0.5
λLT < λL0
Beams without full lateral restraint
No
High shear
Plastic & compact :Mc = py S
Low shear
Moment capacity Mc
αLT = 7 Robertson Constant
Lateral‐ torsional ΦLT = [py + (ηLT + 1) pE] / 2 buckling factor
pb = [(pE * py)/ ΦLT+(ΦLT2‐pE * py)0.5] Mb = pbS :Plastic & compact Mb = pbZ :Semi ‐ compact
M < Mb/ mLT M < Mc M : Factored moments mLT : Equivalent uniform moment factor = 1
Compression Members Structural members subjected to compressive loads, either fail due to Yielding ‐ Compressive stress exceeding the yield strength Buckling ‐ Lateral deflection
P Initial imperfections approximated with a sine curve.
In real columns, always some initial imperfections exist prior to loading. The formula for compressive strength in the BS standard pc = [(pE * py)/ Φ+(Φ2‐pE * py)0.5] is based on the Perry Robertson formula derived from the expression for the maximum stress in an axially loaded initially curved column Compressive strength factor
Φ = [py + (η + 1) pE]/2
The Perry factor (For flexural buckling under axial force)
η = a(λ – λ0)/1000
yo y
Robertson performed many tests on struts to arrive at a suitable value for the initial imperfections ‘η’ Based on this BS5950 provides four values of ‘a’ that may be used in design a = 2.0 ‐ strut curve (a) a = 3.5 ‐ strut curve (b) a = 5.5 ‐ strut curve (c) a = 8.0 ‐ strut curve (d) Depending on types of steel section & axis about which buckling may occur.
As can be seen, the higher the value of a, more initial imperfection is accounted for and the compressive strength reduces as a result.
P
Compression Members Compression resistance Pc
Plastic & compact Semi‐compact
No If section is Yes Slender ?
Pc = pc Ag
Equivalent slenderness
a = 2.0 ‐ strut curve (a) a = 3.5 ‐ strut curve (b) a = 5.5 ‐ strut curve (c) a = 8.0 ‐ strut curve (d)
Elastic critical stress
Compressive strength
Slender
λeff =λ(Aeff /Ag)0.5
Reduced slenderness ratio
λ0 = 0.2(π2E/py)0.5
Limiting slenderness
Robertson constant
λ = kL / r
Pc = pcs Aeff
pE = π2E/λ2
pc = [(pE * py)/ Φ+(Φ2‐pE * py)0.5]
Perry factor η= a (λ‐λo) /1000
Φ = [py + (η + 1) pE] / 2
Lateral‐ torsional buckling factor
Combined Axial force and Moment For cross section capacity Ref. Cl. 4.8.3.2
M Fc M + x + y ≤1 Ag p y M cx M cy
For member Buckling Resistance Fc m x M x m y M y + + ≤1 Simplified method Pc pyZ x pyZ y
Ref. Cl. 4.8.3.3.1
Exact method Ref. Cl. 4.8.3.3.2
Fc m LT M LT m y M y + + ≤1 Pcy Mb pyZ y
Fc m x M x + Pcx M cx
⎛ F ⎜⎜1 + 0.5 c Pcx ⎝
Fc m LT M LT m y M y + + Pcy Mb M cy
m M ⎞ ⎟⎟ + 0.5 yx y ≤ 1 M cy ⎠
For major axis buckling
⎛ ⎞ ⎜1 + F c ⎟ ≤ 1 ⎜ Pcy ⎟⎠ ⎝
For lateral ‐ torsional buckling
m x M x (1 + 0.5(Fc / Pcx )) m y M y (1 + Fc Pcy ) + ≤1 M cx (1 − Fc Pcx ) M cy (1 − Fc Pcy )
For interactive buckling
References 1.
‘Steel Designers’ manual’, 5th Edition by Owens G.W and Knowles P. The Steel Construction Institute, Blackwell Scientific Publishers.
2.
Timoshenko S.P. and Gere J.M., ‘Theory of Elastic Stability’,2nd Edition McGraw Hill Book Company.
3.
Bulson, P.S. The Stability of Flat Plates, Elsevier, New York, 1969.
4.
‘Guide to Stability Design Criteria for Metal Structures’ The Structural Stability Research Council. Theodore V. Galambos.
5.
Gaylord E. H. et al, ‘Design of Steel Structures’, McGraw Hill.
