Ground Floor Beam

8/11/2019 Ground Floor Beam

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Ground Floor Beam and Checking

(1/A-B)G and (4/A-B)G

Dead Load (DL):

Slab Weight (150 mm) (Assume) = (3.8 KN/m2X 2.5m) = 9.500 KN/m

Finishing/Flooring = (1.0 KN/m2X 2.5m) = 2.500 KN/m

Ceiling = (0.6 KN/m2X 2.5m) = 1.500 KN/m

Mechanical & Electrical = (0.5 KN/m2X 2.5m) = 1.250 KN/m

Brick Wall = (4.35 KN/m2

X 3.5m) = 15.23 KN/m

Self-weight of Beam (Assume) = (1.8 KN/m) = 1.800 KN/m

31.780 KN/m

Live Load (LL):

Lobby = (5.0 KN/m2x 2.5m) = 12.500 kN/m

12.500 kN/m

Design Load = (DLX1.4) + (LLX1.6)

= (31.780 KN/m X 1.4) + (12.50 KN/m X 1.6)

=64.49 KN/m

Vmax=

Mmax=


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(2/A-B)Gand (3/A-B)G

Dead Load (DL):






31.03 KN/m

Live Load (LL):

Lobby = (5.0 KN/m2x 5m) = 25.00 KN/m

25.00 KN/m


= (31.03 KN/m X 1.4) + (25.00 KN/m X 1.6)

= 83.44 KN/m

Vmax=

Mmax=


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(1/C-D)G

Dead Load (DL):





Brick Wall = (4.35 KN/m2X 3.5m) = 15.23 KN/m


31.780 KN/m

Live Load (LL):

Security room = (2.5 KN/m2x 2.5m) = 6.250 kN/m

6.250 kN/m


= (31.780 KN/m X 1.4) + (6.25 KN/m X 1.6)

=54.492 KN/m

Vmax=

Mmax=


4/24

(2/C-D)Gand (3/C-D)G

Dead Load (DL):






31.03 KN/m

Live Load (LL):

Cafetria = (2.0 KN/m2x 5m) = 10.00 KN/m

10.00 KN/m


= (31.03 KN/m X 1.4) + (10.0 KN/m X 1.6)

= 59.44 KN/m

Vmax=

Mmax=


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(4/C-D)G

Dead Load (DL):







31.780 KN/m

Live Load (LL):

Cafeteria = (2.0 KN/m2x 2.5m) = 5.0 kN/m

5.0 kN/m


= (31.780 KN/m X 1.4) + (5.0 KN/m X 1.6)

=47.492 KN/m

Vmax=

Mmax=


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(1/B-C)G

Dead Load (DL):







Allow for partition =

= 2.960 KN/m

34.74 KN/m

Live Load (LL):

Washroom = (2.0 KN/m2x 2.5m) = 5.00 kN/m

5.00 kN/m


= (34.74 KN/m X 1.4) + (5.00 KN/m X 1.6)

= 56.64 KN/m

Vmax=

Mmax=


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(2/B-C)G

Dead Load (DL):





Brick partition (Internal) = (2.5 KN/m2X 3.5m) = 8.75 KN/m



= 2.960 KN/m

43.01 KN/m

Live Load (LL):

Washroom = (2.0 KN/m2x 2.5m) = 5.000 KN/m

Corridor = (2.0 KN/m2x 2.5m) = 5.000 KN/m

10.00 KN/m


= (43.01 KN/m X 1.4) + (10.00 KN/m X 1.6)

= 76.21 KN/m

Vmax=

Mmax=


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(3/B-C)G

Dead Load (DL):





Staircase = (9.0 KN/m2X 2.5m) = 22.500 KN/m



= 2.960 KN/m

56.76 KN/m

Live Load (LL):


Staircase = (4.0 KN/m2x 2.5m) = 10.000 KN/m

15.00 KN/m


= (56.76 KN/m X 1.4) + (15.00 KN/m X 1.6)

= 103.46 KN/m

Vmax=

Mmax=


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(4/B-C)G

Dead Load (DL):






Staircase = (9.0 KN/m2

X 2.5m) = 22.500 KN/m



= 2.960 KN/m

57.24 KN/m

Live Load (LL):


Staircase = (4.0 KN/m2x 2.5m) = 10.000 KN/m

15.00 KN/m


= (57.24 KN/m X 1.4) + (15.00 KN/m X 1.6)

= 104.14 KN/m

Vmax=

Mmax=


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(4/B-C)G-G

Dead Load (DL):


Staircase = (9.0 KN/m2X 2.5m) = 22.500 KN/m


31.91 KN/m

Live Load (LL):

Staircase = (4.0 KN/m2

x 2.5m) = 10.000 KN/m

10.00 KN/m


= (31.91 KN/m X 1.4) + (10.00 KN/m X 1.6)

= 60.67 KN/m

Vmax=

Mmax=


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Summary

Using steel Grade S275 = 275 N/mm2

Beam Without Self-Weight of

Beam

Plastic Modulus,

Sx(cm3)

Sx=

Section Designation

Vmax(KN) Mmax(KN.m)

(1/A-B)G 386.94 1160.82 4221.16 610x305x149

(2/A-B)G 500.64 1501.92 5461.53 615x305x179

(3/A-B)G 500.64 1501.92 5461.53 686x254x152

(4/A-B)G 386.94 1160.82 4221.16 610x305x149

(1/B-C)G 311.52 856.68 3115.20 610x229x125

(2/B-C)G 419.16 1152.68 4191.56 615x305x179

(3/B-C)G 569.03 1564.83 5690.29 762x267x173

(4/B-C)G 572.77 1575.12 5727.70 762x267x173

(4/B-C)G-G 333.69 917.63 3336.84 610x229x125

(1/C-D)G 326.95 980.86 3566.76 610x229x125

(2/C-D)G 380.64 1141.92 4152.44 610x305x149

(3/C-D)G 380.64 1141.92 4152.44 610x305x149

(4/C-D)G 356.64 1069.92 3890.62 610x229x140

For section designation of UB 610 X 305 X 149, the highest shear and moment is use to

check for shear capacity, moment capacity and deflection check. If the highest value of

shear and moment passes the checking, so do the lowest value of shear and moment.

Same goes to section designation of UB 762 X 267 X 173.


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Element UB 610 X 305 X 149 UB 762 X 267 X 173

Depth of section, D (mm) 609.6 762

Web thickness, t (mm) 11.9 14.3

Flange thickness, T (mm) 19.7 21.6Root Radius, r (mm) 16.5 16.5

Depth between Fillets, d (mm) 537.2 685.8

Ratio for buckling flange, b/T 7.74 6.17

Ratio for buckling web, d/t 45.1 48

Second moment of area, Ix(cm4) 125000 205000

Radius of gyration, rx(cm) 25.6 30.5

Elastic modulus, Zx(cm3

) 4090 5390Plastic modulus, Sx(cm

3) 4570 6200

Area of section, A (cm2) 190 2200

Source: BS 5950-1: 2000 (BS 4-1: 2005)

BS 5950-1: 2000 Table 9

Checking for UB 762 X 267 X 173 (Vmax = 572.77 KN; Mmax = 1575.12 KNm)

Assumed the UB section is rolled, and its carry plaster finish.

BS 5950-1: 2000

Web thickness, t = 14.3 < 16 mm, py= 275 N/mm2

Flange thickness, T = 21.6 < 40 mm, py= 265 N/mm2

The parameter, Flange, b/T = 6.17 < 9

Class 1 Plastic

Web, d/t = 48 < Class 1 PlasticHence, the section is categorized as plastic.

Table 9

Table 11


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Shear Capacity, Pv= 0.66pyAv , Av= tD

= 0.6(265)(14.3 x 762)

= 1732.56 KN

Maximum design shear, Vmax

= 572.77 KN

Since Vmax Pv[Safe!]

Hence, design shear is within allowable limits

Since d/t = 48 mm < 70[Rolled] Shear buckling check is

not necessary

Clause 4.2.3

Clause 4.4.5

Moment Capacity, Mc

Vmax 0.6 Pv[Low Shear] ; Vmax > 0.6 Pv [High Shear]572.77 KN 1039.54 KN [Low Shear]

Previously, the section was categorized as plastic.

Hence, Moment Capacity, Mc= pyS

Moment Capacity, Mcx=pySx[Considering Major axis, x-x]

Mcx= 265(6200 x 103) = 1643 KNm

Maximum design moment, Mmax= 1575.12 KNmSince Mmax Mcx [Safe!]

Hence, design moment is within allowable limits

To avoid deflection Mcx 1.2 pvZx:

1643 KNm 11206.2 KNm

Hence, Mcx= 1643 KNm

Clause 4.2.5

Clause 4.2.5.1

Deflection of beam

The maximum unfactored imposed load is 17.5 KN/m

Therefore, the serviceability loads may be taken as

unfactored imposed load, 1= 17.5 KN/m

Clause 2.5


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Second moment of area, Ix= 205000 cm4= 0.00205 m4

Youngs modulus, E = 205 kN/mm2= 205 x 106KN/m2

Longest Span of beam = 12 m

Beam carrying plaster finish,

Deflection limit, Since, < Deflection is within the allowablelimit.

Table 8

Web Bearing

= t + 1.6r + 2T = 14.3 + 1.6(16.5) + 2(21.6) = 83.90mm

K = T + r = 21.6 + 16.5 = 38.1 mm [Rolled]

= [83.90 + (2 x 38.1)](14.3)(275) = 629.59 KN

Since, Vmax< [Safe!]Bearing Stiffener is not required

Clause 4.5.2

Web Buckling

= 41.95 mm,0.7d = 0.7 (685.8) = 480.06 mm

Since ae< 0.7d,

Web buckling resistance, Px=

()

= 582.18 KN


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Since Vmax< Px[Safe!]

Safe against buckling. Load carrying stiffener is not

required.

Checking for UB 610 X 305 X 149 (Vmax= 386.94 KN; Mmax= 1160.82 KNm)


BS 5950-1: 2000


Flange thickness, T = 19.7 < 40 mm, py= 265 N/mm

2

The parameter, Flange, b/T = 7.74 < 9 Class 1 PlasticWeb, d/t = 45.1 < Class 1 PlasticHence, the section is categorized as plastic.

Table 9

Table 11


= 0.6(265)(11.9 x 609.6)

= 1153.42 KN

Maximum design shear, Vmax= 386.94 KN



Since d/t = 45.1 mm < 70[Rolled] Shear buckling check

is not necessary

Clause 4.2.3

Clause 4.4.5

Moment Capacity, Mc

Vmax 0.6 Pv[Low Shear] ; Vmax > 0.6 Pv [High Shear]

Clause 4.2.5


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386.94 KN 692.05 KN [Low Shear]




Mcx= 265(4570 x 103) = 1211.05 KNm

Maximum design moment, Mmax= 1160.82 KNm

Since Mmax Mcx [Safe!]



1160.82 KNm 1300.62KNm

Hence, Mcx= 1160.82 KNm

Clause 4.2.5.1

Deflection of beam

The maximum unfactored imposed load is 17.5 KN/m

Therefore, the serviceability loads may be taken as

unfactored imposed load, 1= 17.5 KN/m

Second moment of area, Ix= 125000 cm4= 0.00125 m4

Youngs modulus, E = 205 kN/mm2= 205 x 106KN/m2

Longest Span of beam = 12 m

Beam carrying plaster finish,

Deflection limit,

Since, < Deflection is within the allowablelimit.

Clause 2.5

Table 8

Web Bearing

Clause 4.5.2


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= t + 1.6r + 2T = 11.9 + 1.6(16.5) + 2(19.7) = 77.70mm

K = T + r = 19.7 + 16.5 = 36.2 mm [Rolled]

= [77.70 + (2 x 36.2)](11.9)(275) = 491.20 KN


Web Buckling

= 38.85 mm,

0.7d = 0.7 (537.2) = 376.04 mm

Since ae< 0.7d,


()

= 280.97 KN

=

= 8804.66 KN



required.


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(D/1-2)G , (D/2-3)G, (D/3-4)G, (A/1-2)G, (A/2-3)G, (A/3-4)G

Dead Load (DL):



15.530 KN/m


= (31.780 KN/m X 1.4) + (0 X 1.6)

=21.74 KN/m

Vmax=

Mmax=

(B/1-2)G , (B/2-3)G, (B/3-4)G, (C/1-2)G, (C/2-3)G, (C/3-4)G

Dead Load (DL):

Brick partition (Internal) = (2.5 KN/m2X 3.5m) = 8.750 KN/m


9.050 KN/m


= (9.050 KN/m X 1.4) + (0 X 1.6)

=12.67 KN/m

Vmax=

Mmax=


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Summary

Using steel Grade S275 = 275 N/mm2

Beam Without Self-Weight of

Beam

Plastic Modulus,

Sx(cm3)

Sx=

Section Designation

Vmax(KN) Mmax(KN.m)

(A/1-2)G 54.35 67.94 247.16 203 x 133 x 30

(A/2-3)G 54.35 67.94 247.16 203 x 133 x 30

(A/3-4)G 54.35 67.94 247.16 203 x 133 x 30

(B/1-2)G 31.68 39.59 143.96 203 x 102 x 23

(B/2-3)G 31.68 39.59 143.96 203 x 102 x 23

(B/3-4)G 31.68 39.59 143.96 203 x 102 x 23

(C/1-2)G 31.68 39.59 143.96 203 x 102 x 23

(C/2-3)G 31.68 39.59 143.96 203 x 102 x 23

(C/3-4)G 31.68 39.59 143.96 203 x 102 x 23

(D/1-2)G 54.35 67.94 247.16 203 x 133 x 30

(D/2-3)G 54.35 67.94 247.16 203 x 133 x 30

(D/3-4)G 54.35 67.94 247.16 203 x 133 x 30

Element UB 203 x 102 x 23 UB 203 x 133 x 30

Depth of section, D (mm) 203.2 206.8

Web thickness, t (mm) 5.2 6.3

Flange thickness, T (mm) 9.3 9.6

Root Radius, r (mm) 7.6 7.6Depth between Fillets, d (mm) 169.4 172.3

Ratio for buckling flange, b/T 5.46 6.97

Ratio for buckling web, d/t 32.6 27.3

Second moment of area, Ix(cm4) 2090 2890


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Radius of gyration, rx(cm) 8.49 8.72

Elastic modulus, Zx(cm3) 206 279

Plastic modulus, Sx(cm3) 232 313

Area of section, A (cm

2

) 29 38Source: BS 5950-1: 2000 (BS 4-1: 2005)

BS 5950-1: 2000 Table 9

Checking for UB 203 x 133 x 30 (Vmax = 54.35 KN; Mmax = 67.34 KNm)


BS 5950-1: 2000




Table 9

Table 11


= 0.6(275)(6.3 x 206.8)

= 214.97 KN





is not necessary

Clause 4.2.3

Clause 4.4.5


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Moment Capacity, Mc


54.35 KN 128.98 KN [Low Shear]




Mcx= 275(313 x 103) = 86.08 KNm





86.08 KNm 92.07 KNm


Clause 4.2.5

Clause 4.2.5.1

Deflection of beam

Because the BS code required unfactored imposed load (live

load), since this is one-way slab, no imposed load is being

transfer to this vertical beam, hence, the deflection is

zero.

Clause 2.5

Web Bearing

= t + 1.6r + 2T = 6.3 + 1.6(7.6) + 2(9.6) = 37.66 mmK = T + r = 9.6 + 7.6 = 17.2 mm [Rolled]

= [37.66 + (2 x 17.2)](6.3)(275) = 124.84 KN


Clause 4.5.2


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Web Buckling

= 18.83 mm,0.7d = 0.7 (172.3) = 120.61 mm

Since ae< 0.7d,


()

= 102.00 KN

Since Vmax< Px[Safe!]Safe against buckling. Load carrying stiffener is not

required.

Checking for UB 203 x 102 x 23 (Vmax = 31.68 KN; Mmax = 39.59 KNm)


BS 5950-1: 2000




Table 9

Table 11

Shear Capacity, Pv= 0.66pyAv , Av= tD Clause 4.2.3


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= 0.6(275)(5.2 x 203.2)

= 174.35 KN


Since Vmax

Pv[Safe!]



is not necessary

Clause 4.4.5

Moment Capacity, Mc


31.68 KN 104.61 KN [Low Shear]




Mcx= 275(232 x 103) = 63.80 KNm





63.80 KNm 67.98 KNm


Clause 4.2.5

Clause 4.2.5.1

Deflection of beam

Because the BS code required unfactored imposed load (live

load), since this is one-way slab, no imposed load is being

transfer to this vertical beam, hence, the deflection is

zero.

Clause 2.5

Web Bearing Clause 4.5.2


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= t + 1.6r + 2T = 5.2 + 1.6(7.6) + 2(9.3) = 35.96 mmK = T + r = 9.3 + 7.6 = 16.90 mm [Rolled]

= [35.96 + (2 x 16.90)](5.2)(275) = 99.76 KN


Web Buckling

= 17.98 mm,

0.7d = 0.7 (169.4) = 118.58 mm

Since ae< 0.7d,


()

= 69.43 KN



required.

Ground Floor Beam

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