Design of Moment connection (Welded Type)

Beam Properties : ISB 113.5x113.5x4.5 Column Properties : ISMC 200

2
A = 3233.00 mm Dcol = 200 mm
h = 200.00 mm bfcol = 100 mm
d = 178.40 mm dcol = 178.4 mm
bf = 100.00 mm twcol = 5.7 mm
b = 50.00 mm tfcol = 10.8 mm
tw = 5.70 mm
tf = 10.80 mm
4
Ixx = 22354000 mm
3
Ze(xx) = 223500 mm
3
Zp(xx) = 253860 mm
r = 11 mm

Steel Properties :
Grade of Steel = E250A (PDRP-8320-SP-0016)
Yield Stress (Min) = 250 MPa IS:800-2007 Table 1 & IS:2062)
Ultimate Tensile Stress(min) = 410 MPa (IS:800-2007 Table 1 & IS:2062)
Connection is Designed for 100 % moment capacity of section
gm0 = 1.1 (IS:800-2007 Table 5, Cl 5.4.1)

gmw = 1.25 (Shop Fabrications) (IS:800-2007 Table 5, Cl 5.4.1)

= 1.5 (Field Fabrications) ( IS:800-2007 Table 5, Cl 5.4.1)
gml = 1.25 (IS:800-2007 Table 5, Cl 5.4.1)
Legend :
h = Overall depth of section
fyw = Yield Strength of the web
Aw = Shear Area
ε = Constant (Depending of yield Stress)
Vd = Design Shear Strength
gm0 = Partial safety factor (Resistance, governed by yielding)
gmw = Partial safety factor (Resistance of connection Welds)
gml = Partial safety factor (Resistance governed by ultimate stress)
Section Classification (Refer IS:800-2007, Cl 3.7.2,Cl.3.7.4, Table 2) :

250 250
ε =
fy
=
250

ε = 1
bf / t f = 4.63 < 9.4 ε
h/tw = 31.30 < 84 ε

Section is Plastic Section(Class 1)

Design Forces :
a) Shear capacity of beam : (IS:800-2007, Cl.8.4.1)

Aw x fyw
Vd =
3 gm0
Where,
fyw = 250
 Aw = h x tw
= 200 x 5.7
Aw = 1140

Vd = 1140 x 250
3 x 1.1
Vd = 149586 N
Vd = 149.59 kN
0.6Vd = 89.75 kN

b) Moment capacity of beam : (IS:800-2007, Cl.8.2.1)

Check for web buckling under shear before yielding

h/tw = 35.09 < 67 ε

Section is safe in web buckling

Assuming, if V ≤ 0.6Vd
βb Zp fy 1.5 Ze fy (IS:800-2007,Cl.8.2.1.2)
Md = <
gm0 gm0

Where,
βp = 1
1 x 253860 x 250
Md =
1.1

= 5.770E+07 N-mm < 6.095E+07 N-mm

Md = 57.70 kN-m < 60.95 kN-m

Hence, Section is safe in irreversible deformation under serviceability loads

Design forces summary
Connection is designed for 100 % Moment Capacity of Section & 60 % Shear Capacity of Section

Shear Capacity = 89.00 kN

Moment Capacity = 1.2 x Md (IS800-2007, Cl.12.11.2.1)
Moment Capacity = 70.00 kN-m
3
Flange Force Md 70.00 x 10
= =
h 200
Flange Force = 350.00 kN

Calculation for width of cover plate (B1 & B2)

i) Top cover plate width

Width of top cover plate B1 = Flange width - 2 x Size of weld - 10
Assume size of weld (W1) = 8 mm
= 100 - 16 - 10
= 74 mm
Say, B1 = 70 mm

ii) Bottom cover plate width

Width of bottom cover plate B2 = Flange width + 2 x Size of weld + 10

Assume size of weld (W2) = 8 mm
= 100 + 16 + 10
= 126 mm
Say, B2 = 150 mm
Thickness calculation for Cover Plates (T1 & T2)

Design strength in tension (Tdn) (IS:800-2007,Cl.6.3.1)

0.9 An fu
Tdn =
gml

0.9 x An x 410
350 x 103 =
1.25

An = 1185.64 mm2

Flange width of beam = 100 mm B1' B1

B1' = Flange width of beam = 100 mm

Therefore, thickness of cover plate

1185.64
Top Cover Plate T1 = = 11.85637
100
= 12 mm > Thickness of Flange 10.8 mm

1185.64
Top Cover Plate T2 = = 7.904246
150
= 10 mm < Thickness of Flange 10.8 mm

Hence provide thickness of cover plates ( T1 and T2 )

T1 = 12 mm
T2 = 12 mm

Calculation for length of cover plate (L1 & L2)

Size of weld for top & bottom plate respectively

W1 = 8 mm
W2 = 8 mm
a = weld length
t = 0.7s = Effective throat thickness of weld

i) Top cover Plate

Equating,
Weld Strength = Tensile Force
fu
(2 x a + 70 ) x t x = 350 x 103
3 gmw

3.500E+05 x 3 x 1.5
(2 x a + 70 ) x k x s =
410

(2 x a + 70 ) x 0.7 x 8 = 2217.87 (IS800-2007,Cl.10.5 &

Table 22 , k = 0.7 )
a = 163.02 mm

say, a = 170 mm

Total weld length provided = 410 mm < 150 t = 840 mm

Check for reduction in design strength of weld (IS800-2007,Cl.10.5.7.3)

0.2 lj
Reduction factor = 1.2 - ≤ 1.0
150 t
 Where,
lj = 340 mm
= 1

Hence no need to reduce design capacity as per IS:800-2007 Cl. 10.5.7.3

Weld length after reduction in design strength of weld

a = 170 mm

ii) Bottom cover Plate

Equating,
Weld Strength = Tensile Force
fu
2xa xtx = 350.00 x 103
3 gmw

3.500E+05 x 3 x 1.5
2xa x k x s =
410

2 x a x 0.7 x 8 = 2217.87 (IS800-2007,Cl.10.5 &

Table 22 , k = 0.7 ) )
a = 198.02 mm

say, a = 200 mm

Total weld length provided = 400 mm < 150 t = 840 mm

Check for reduction in design strength of weld (IS800-2007,Cl.10.5.7.3)

0.2 lj
Reduction factor = 1.2 - ≤ 1.0
150 t
Where,
lj = 400 mm
= 1.000

Hence no need to reduce design capacity as per IS:800-2007 Cl. 10.5.7.3

Weld length after reduction in design strength of weld

a = 200 mm

Hence, Provide Length of Top & Bottom cover plates

L1 = 200 mm
L2 = 200 mm

Design of Bearing Bracket

i) Design of Width of Bearing Plate (L3)

a) Safe Crippling Length

fyw
Fw = (b1+n2) tw (IS800:2007,Cl.8.7.4)
gm0

where,
b1 = L3 = Bearing Bracket Length
 tw = 5.7 mm
fyw = 250 MPa
Fw = 89.00 kN
n2 = 2.5 x 10.8 + 11
= 38 mm

89.00 = (L3 + 38 ) x 5.7 x ( 250 / 1.1 )

(L3 + 38 ) = 89000.00
5.7 x ( 250 / 1.1 )

L3 = 30.70 mm

b) Safe Buckling Length

Fcdw = (b1+n1) tw fcd (refer IS800:2007,Cl.8.7.4)

where,
b1 = L3 = Bearing Bracket Length
tw = 5.7 mm
Fcdw = 89.00 kN
n1 = 0.5h
= 100 mm
Design Compressive Stress (fcd) Calculation
(IS800:2007,Table 9(a))
h/bf = 2.00 > 1.2
tf = 10.8 < 40

Section has Buckling Class a @ z-z axis

(IS800:2007,Table 10)

Iy
ry = of web
A

[(b1+n1) tw3]/12
=
(b1+n1) tw

ry = tw / 2 3

l = Leff / ry
Leff = 0.7d (IS800-2007 Cl. 8.7.1.5)

l = 0.7 d x ( 2 3/ tw)
l = 2.5 (d/tw)
= 78.24561
Therefore,
fcd = 167 (Refer Table 9 )
89.00 = (L3 + 100 ) x 5.7 x 167

(L3 + 100 ) = 89 / ( 5.7 x 167 )

L3 = -6.50 mm

Hence provide width of bearing plate L3 = 150 mm

ii) Design of depth of Bearing Plate (D)

n Lw t f u
Design strength of weld =
3 gmw
Where,
Lw = Eff. Length of weld
t = Throat thickness
fu = 410 MPa
gmw = 1.25 (Shop Weld)
n = 2 (weld lines)
Assume, Size of weld (W3) = 8 mm
Equating,
Shear force = Weld Strength

2 x Lw x 0.7 x 8 x 410
89.00 x 103 =
3 x 1.25

Lw = 89000 x 3 x 1.25
2 x 0.7 x 8 x 410

Lw = 41.96 mm

Hence provide length of bearing bracket

D = 225.00 mm

Check for Eccentric Shear

Section modulus of weld group

Zw = 2 t D2/6

= 2 x 0.7 x 8 x 225 x ( / 6 )

Zw = 94500.00 mm3

Shear force 89 x 1000

Direct Shear Stress (q) = =
2xDxt 2 x 225 x 0.7 x 8

q = 35.32 MPa

M Shear force x e
Bending Stress (fa) = =
Zw Zw

Where,
e = L3 / 2
= 75.00 mm

89 x 1000 x 75
=
94500.00

(fa) = 70.63 MPa

Resultant stress (Refer IS:800-2007,Cl 10.5.10.1.1)

fe = fa2 + 3q2 ≤ fu
3 gmw
= 70.63 + 3 x 35.32 ≤ 410
3 x 1.25

= 93.44 MPa < 189.37 MPa

……...Hence ok

iii) Design of thickness of Bearing Plate (T3)

a) From Bearing Consideration

Equate,
Load transferred = Bearing strength of stiffener
Fx = Fpsd

Aq fyq (Refer IS:800-2007,Cl.8.7.5.2)

89.00 x 103 =
0.8 gm0
Where,
Aq = Area of stiffener
fyq = yield stress

Aq 89 x 1000 x 0.8 x 1.1

=
250
Aq = 313.28 mm2

Thickhess of bracket (T3) = Area of bracket/ Width of bracket

= 2.09 mm

b) From Beam Shear Consideration

T3 = Max of
i) Thickness of web of beam = 5.7 mm
ii) 2 x Throat thickness = 11.2 mm
Therefore,
T3 = 11.2 mm

Hence provide thickness of bearing plate (T3) = 12 mm

…..Hence OK

Check for shear & Bending stresses

i) Shear Stress

tab = Vs < fy
td 3
Where,
Vs = 89.00 kN
t = T3 = 12 mm
d =D = 225 mm

89 x 1000
=
12 x 225
tab = 32.96 MPa < 144.34 MPa
 ii) Bending Stress
Ms fy
fbc = <
Zec gm0

Where,
Ms = Vs x e
e = L3 / 2
= 75.0 mm

Zec T3 x D2
=
6
3
Zec = 101250 mm

89 x 1000 x 75
fbc =
101250

= 65.9 MPa < 227.27 MPa

…..Hence OK

Design of Doubler Plate (Refer Cl 12.11.2.4 & 12.11.3.3)

i) Design of thickness of Doubler Plate (tdp)

As per Cl. 12.11.2.4 thickness of doubler plates shall satify following cariteria
Doubler Plate
(bdp x tdp)
(dp + bp)
tdp ≥
90

( 178.4 + 178.4 ) dp
=
90

bp
= 3.96444 mm

Provide thickness of doubler plate = 25 mm

Check for buckling of Plate

As per Cl. 12.11.3.3 Doubler Plates shall resist at least 2 % of Flange force

2 % of Flange force = 7 kN

Fcdw = (b1+n1) tdp fcd

(refer IS800:2007,Cl.8.7.4)

where,
b1 = dcol = 178.4 mm
tdp = 25 mm
n1 = 0.5dcol
= 89.2 mm
fcd (refer IS800:2007,Table 9(a)
Dcol/bfcol = 2.00 > 1.2
tf = 10.8 < 40

Section has Buckling Class a @ z-z axis

(refer IS800:2007,Table 10)

Iy
ry = of doubler plate
A
 [(bdptdp3]/12
=
bdp x tdp

ry = tdp / 2 3

l = Leff / ry
Leff = 0.7dcol (Refer Cl. 8.7.1.5)

l = 0.7 dcol x ( 2 3/ tdp)

l = 2.5 (dcol/twcol)
= 17.84 mm
Therefore,
fcd = 101 Refer Table 9 of IS800

Fcdw = 675.69 kN > 7 kN

Hence thickness of dubler plate provided is ok

Check for bearing of Plate

Aq fyq (Refer IS:800-2007,Cl.8.7.5.2)

Fpsd =
0.8 gm0
Where,
Aq = bdp x tdp
= [( 100 - 5.7 )/2] x 25
2
= 1178.75 mm
fyq = yield stress
= 250 MPa

Fpsd 1178.75 x 250

=
0.8 x 1.1

Fpsd = 334.87 kN > 7 kN

Hence thickness of dubler plate provided is ok

Check for Column Web Thickness

As per Cl. 12.11.2.4 thickness of column web shall satify following cariteria

(dp + bp)
tdp ≥
90

( 178.4 + 178.4 )
=
90

= 3.96444 mm < Column Web Thickness = 5.7 mm

………...Hence OK
.
Summary of Connection Design
Beam Mark = ISB113.5x113.5x4.5
Top Cover Plate
Width (B1) = 70 mm
Length (L1) = 200 mm
Thickness (T1) = 12 mm

Bottom Cover Plate

Width (B2) = 150 mm
Length (L2) = 200 mm
Thickness (T2) = 12 mm

Bearing Bracket
Width (L3) = 150 mm
Depth (D) = 225 mm
Thickness (T3) = 12 mm
Welds
W1 = 8 mm
W2 = 8 mm
W3 = 8 mm