Design Calculation Job No: IA-PB-****

Design By : ***

Checked By : ***

Page # : 1

Reference Codes

IRC-22

IRC-24

IRC-21

GIVEN DATA

Span (L) = 18 m

Concrete slab width (cbf) = 2000.00 mm

Thickness of slab (cth) = 300.00 mm

fck, Grade of concrete = 40 N/mm2

Live Load (LL) = 700.00 kN

Super imposed dead load = 20% slab wt

Steel Beam I- Section

dw, Web Depth = 1000 mm

tw, Web Thickness = 10 mm

bf, Flange Width = 500 mm

tfo, Flange Thickness = 30 mm

bf, Bottom Flange Width = 500 mm

tfi, Bottom Flange Thickness = 30 mm

D, Total Depth = 1060 mm

Type of Construction : Unshored

DATA ASSUMED

Ec = 32500 N/mm2

(IRC-21:2000, Table-9)

Density of Concrete = 24 kN/m3

Es, Modulus of Elasticity = 211000 N/mm2

(IRC-24:2001, 505.1.1)

Density of steel = 78.5 kN/m3

Yield strength of steel 250 Mpa

Y

Concrete Flange = 2000 x 300

Z Z

Web =1000x10

Top & Bottom Flange=500x30

Y

Load Calculation

Dead Loads

Self weight of slab = 14.40 kN/m

Self weight of beam = 3.14 kN/m

Super imposed dead load ( 20% slab wt ) = 2.88 kN/m

Total Dead Load (DL) = 20.42 kN/m

DL moment ( wl^2/8) = 827.01 kN.m

LL moment ( Wl / 8) = 1575.00 kN.m

DL Shear 183.78 kN

LL Shear 350.00 kN

Design Calculation Job No: IA-PB-****

Design By : ***

Checked By : ***

Page # : 2

M, Moment = wL2/8 = 583.2 kN.m

V, Shear Force = 129.6 kN

Modular Ratio

For Permenant Loads, m = Es / ( Kc x Ec ) = 12.98461538

For Transient Loads, m = Es / ( Ec ) = 6.492307692

Properties of I - Beam (STEEL)

A, Area = 40000 mm2

yg, centroid of section from bottom flange = 530 mm

Iz, Inertia about major axis = 8,792,333,333 mm4

Iy, Inertia about minor axis = 625,083,333 mm4

ry Radius of gyration about yy 125

Z, Section Modulus 16,589,308 mm3

Composite proerties for Transient Loads

transformed Effective width of flange ( cbf/m) = 308.06 mm

transformed Area for concrete flange () = 92417 mm2

Design Calculation Job No: IA-PB-****

Design By : ***

Checked By : ***

Page # : 3

Combined Properties of I-beam + Concrete flange

Total Depth = 1360 mm

Total area = 132417 mm2

C. G. of section from bottom flange = 1005 mm

Iz, for combined section = 22,394,265,877 mm4

Zzbottom flange, for combined section = 22,291,981 mm3

Z top, for combined section = 63,009,384 mm3

Calculation of elastic Critical stress fcb

fcb = k1 ( X + k2 Y ) ( c2 / c1 ) 191.72

X = Y sqrt ( 1 + 1/20 ( l T / ( ry D )^ 2 ) 127.814206

Y = 26.5 x 10 ^ 5 / ( l / ry ) ^ 2 Mpa 127.81411

c1, c2 = lesser & greater distance of of extreme

fiber from N.A 530.0 Mpa

k1 1

k2 0.50

sigma bc 87 Mpa

1) Checking of the stress

CONSTRUCTION STAGE

During construction stage, since

Due to Dead Loads ( Unshored condition )

bending compressivestress @ top flange 49.85

Allowable stress

bending tensile stress @ bottom flange = 49.85 N/mm2

Allowable bending stress = 0.62 * Fy = 155 N/mm2

Unity Check = 0.32 < 1.0 Hence ok

Shear stress (average) = 18.38 N/mm2

Allowable shear stress = 0.38 * Fy = 95 N/mm2 ( Table 6.2, IRC-24-2001 )

Unity Check = 0.19 < 1.0 Hence ok

Deflection check

Allowable deflection ( span / ) = 600

Deflection ((5/384)*w*L4/(E*I) = 5.9070 mm

span / deflection = 3047 O.K.

Composite action for additional live load

Additional tesile stress in steel 71 N/mm2

Total tensile stress in steel 121 N/mm2

Allowable bending stress = 0.62 * Fy = 155 N/mm2

Unity Check = 0.78 < 1.0 Hence ok

Compressive stress in concrete = 3.85 N/mm2

Allowable stress 15.00 N/mm2 ( Table - 9 of IRC 21)

Vertical Shear

Total Vertical shear is assumed to be resisted by steel beam

Total Vertical shear = 533.78 kN

Shear stress (average) = 53.38 N/mm2

Allowable shear stress = 0.38 * Fy = 95 N/mm2 ( Table 6.2, IRC-24-2001 )

Unity Check = 0.56 < 1.0 Hence ok

Design of shear connectors

High tensile shear Connector from fatigue strength consideration

IRC:22-2000: Cl 611.4.1.2

VR = 350.00 kn

Area of transformed concrete salb = Ac = 92417 mm2

Y bar = 205

I = 22,394,265,877 mm4

Vr 0.2967 kN/mm

P = Spacing of connectors required

Design Calculation Job No: IA-PB-****

Design By : ***

Checked By : ***

Page # : 4

dia of shear stud, d 25

stud height , h 120

h/d 5 > 4

No of shear studs / cross section 2

Qr = Alpha. A. 10^-2 27 kN

P 182 mm

High tesile shear Connector from the consideration of ultimate flexural strength

Maximum horizontal force based on CL 611.4.1.2.1

H1 = Ast . Fy . 10-3

= 10000 kN

H2 = 0.85 fc. bf. hf. 10-3

20400 kN

Maximum horizontal force in the slab =minimim of H1 & H2

10000 kN

The ultimate strength of shear connector Qu = 0.5A sqrt (fck.Ec) x 10^-3

279.84

number of shear connectors between the mid span and end support, n = H/ ( lamda Qu ), Lamda = 0.85

42.04

The number of shear connecters based on fatigue 98.91 Hence the fatigue strength requirement governs

Design of transverse reinforcement

VL = V . Ac . Y / I

Since it is unshored construction, the V is the shear from Live load & super imposed dead load

350.00

VL 0.30 kN/mm

0.4 Ls sqrt (fck)

Ls, length of shear plane 1-1 as per Fig 5a of IRC 22

600 mm

Ls, for shear plane 2-2 as per Fig 5a of IRC 22 740 mm

0.4 Ls sqrt (fck) 1517.89

0.7 As sigma y + 0.08 Ls sqrt (fck) 486.01

Reinforcement provided = 0.2% in each direction 600.00 mm^2 / m length

Diameter of reinforcement 10.00 mm

spacing of top & bottom bar 0.26 m

Provide 10mm dia bars @ 250k=mm spacing at top & bottom in both directions