Beam.xls

(1)

DESIGN CALCULATIONS

REFERENCES /REFERENCES /

REMARKS REMARKS

Walkway - Main Beam Walkway - Main Beam

G

Grraad

de

e

o

of

f

S

Sttrru

uccttu

urraal

l

sstteeeell

=

43A

D

Deessiig

gn

n

ssttrreen

ng

gtth

h

o

of

f

sstteeeell,

,

p

py

y

=

275.0

275.0 N/mm

N/mm

22

Tb.6, BS:5950, part-1

L

Leen

ng

gtth

h

o

of

f

B

Beeaam

m

=

4.000

4.000 m

m

S

Sp

paacciin

ng

g

o

of

f

b

beeaam

mss,

,

ss

=

1.00

1.00 m

m

B

Been

nd

diin

ng

g M

Mo

om

meen

nt

t cco

o--eeffffiicciieen

nt

t ffo

or

r V

Veerrttiiccaal

l b

been

nd

diin

ng

g

=

8

8 (8 for Simply Supported)

(8 for Simply Supported)

UDL

UDL Deflection

Deflection co-efficient

co-efficient

=

5

5 (5

(5 for Sim

for Simply Supported)

ply Supported)

D

Deefflleeccttiio

on

n F

Faacctto

orr((ssp

paan

n /

/ d

deefflleeccttiio

on

n rraattiio

o))

=

300

300 Table:5,BS 5950,p-1

Table:5,BS 5950,p-1

Loads

UD UD LL

D

Deeaad

d

llo

oaad

ds

s

o

on

n

ffllo

oo

orr,

,

w

wss

=

1.00

1.00 k

kN

N//m

m2

2 S

Seecc..4

4..1

1 &

&

4..2

4

2 o

of

f

IIm

mp

po

osseed

d

llo

oaad

ds

s

o

on

n

ffllo

oo

orr,

,

w

wii

=

10.00

10.00 k

kN

N//m

m2

2 tth

hiis

s

d

do

occu

um

meen

ntt..

C

Co

on

nssttrru

uccttiio

on

n

llo

oaad

ds

s

((tteem

mp

po

orraarry

y)),

,

w

wcc

=

0

0 k

kN

N//m

m2

2 C

Cll..2

2..2

2..3

3,,B

BS

S

5

59

95

50 0,,p

p--4

4 D

Deecck

k

p

prro

offiille

e

sseellf

f

w

wt

t

p

peer

r

m

meettrree,

,

w

wp

p

=

0

0 kN/m2

kN/m2

B

Beeaam

m

sseellf

f

w

wt

t

p

peer

r

m

meettrree,

,

w

wb

b

=

1 1..0

01 1 k

kN

N//m

m

POINT L

POINT LOADS OADS

_P

ii

₍₍

ii

_{= 1,2,3,4)}

a a

Unfactored

1

1 x

x

2

2 Reactions

Reactions

P

P1

1 P

P2

2 P

P3

3 P

P4

4 P

P5

5 P

P6

6 P

P7

7

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 .

.

0

0 R2 = 20.00 kN (Live)

R2 = 20.00 kN (Live)

Dead Load (kN)

Live Load (kN)

Distance

aa

_{from support 1 (m)}

R1 = 20.00 kN (Live)

4

4 .

.

0

3

3 k

k

N

(

D

e

a

d

)

4

4 .

.

0

3

3 k

k

N

(

D

e

a

d

)

Moment value here

E

E D

D P

P C

C O

O N

N S

S U

U L

L T

T I

I N

N G

G G

G R

R O

O U

U P

P SDN

SDN BHD

BHD

C O

(2)

DESIGN

Assume

the

section

as

=

UB

533 x

210 x

101 a) Sectional properties

Depth

of

the

section,

D

=

536.7 mm

Width

of

the

section,

B

=

210.1 mm

Thickness

of

web,

t

=

10.9 mm

Thickness

of

flange,

T

=

17.4 mm

Effective

depth

of

web,

d

=

476.5 mm

Second moment of inertia, I

xx

=

6.17E+08 mm

4

Second moment of inertia, I

yy

=

26900000 mm

4

r

min

=

45.60 mm

Section modulus, Z

xx

=

2300000 mm

3

Section

modulus,

Z

=

257000 mm

3

Plastic modulus, S

xx

=

2620000 mm

3

Plastic modulus, S

yy

=

400000 mm

3

Buckling

parameter,

u

=

0.874 Torsional

index,

x

=

33.1 Torsional

constant,

J

=

1020000 mm

4

Sectional

Area,

A

=

12900 mm2

Out

stand

width

of

panel,

b

=

105.1 mm

Constant,

e,

=

sqrt(275/py)

=

1 Outstand element of

compression flange, b/T

=

6.04 Plastic

Cl.3.5.2 and Table:7

Web

slenderness,

d/t

=

43.72 Plastic

of

BS

5950:part1

b) Design

Loading factor gd, for dead load

=

1.4 Table:2,BS 5950, p-1

Loading factor gl, for live load

=

1.6 Dead load per meter, wd = ws*s + wb (from UDL only)

=

2.014 kN/m

Live load per meter, wl = wi*s (from UDL only)

=

10.000 kN/m

Total working load, (wd+wl) (from UDL only)

=

12.014 kN/m

Ultimate load, (gdwd + gl wl) (from UDL only)

=

18.820 kN/m

Moment fr. UDL plus Moment fr. Point Loads

1

2

3

4

5

6

7 Mid

0.00

37.64

0.00

37.64 Total Ult. Moment (UDL+all Point Load)

Ultimate Moment Due To UDL only (kNm)

Position

(3)

b.2.b)

Since the section is -

Plastic

:Mcx' = py*Sxx

Cl.4.2.5,BS 5950,p-1

=

720.50 kN.m

b.2.c)

However Mcx' shall be limited to

' fo

x

pyZxx '

Cl.4.2.5,BS 5950,p-1

fo

x

=

Elastic

limitation

factors

Cl.4.2.5,BS

5950,p-1

=

1.2 (if shape factor is less than or

equal to 1.2)

=

factored load/unfactored load ( if shape

factor is more than 1.2)

Shape

factor =

Sxx

/

Zxx

=

1.139 <1.2

Hence,

fo

x

=

1.200 Mcx''

=

759.00 kN.m

b.2.d)

Moment Capacity Mcx

= Lesser of Mcx' and Mcx''

=

720.5 kN.m

Satisfactory

>37.64 kN.m

b.3) Check for Deflection

Service Live UDL on major axis,x-x

=

wl

=

10.000 kN/m

Service Dead UDL on major axis,x-x

=

wd

=

2.014 kN/m

Vertical Deflection due to Total Dead Load

0.1 mm

Vertical Deflection due to Total Live Load

=

0.3 mm

Vertical Deflection due to Total Dead Load +

=

0.3 mm

0.8(Live Load)

Allowable

deflection

= L

/300

=

13.3 mm

Satisfactory

>0.3

mm

c) Torsional Buckling Check

c.1) Moment capacity, Mb

c.1.a) Lateral-torsional buckling moment, Mb:

( as per clause 4.3.7.3 of BS 5950, part-1)

Number of lateral supports

=

0 assumed Unbraced

(4)

d) Design of Lateral Restraint

Restraints may be deemed to provide adequate strength if they are capable of resisting a lateral force

Clause 4.3.2, BS5950

of not less than 1% of the maximum factored force in the compression flange or chord.

Ultimate

Moment,

Mu

=

37.64 kNm

Lever

Arm

(D-t)

=

519.3 mm

Maximum factored force in flange, F = Mu/(D-t)

=

72.5 kN

No. of members sharing the restraint

=

2 No. of restraint ponts

=

1 Percentage of maximum factored force

=

1 %

Factored lateral force in restraint member

=

1.4 kN

Assume the restraint member section as

=

UC 305 x 305 x 118

a) Sectional properties

Depth

of

the

section,

d

=

314.5 mm

Width

of

the

section,

b

=

306.8 mm

Thickness,

t

=

11.9 mm

Second moment of inertia, I

xx

=

2.76E+08 mm

4

Second moment of inertia, I

yy

=

90100000 mm

4

r

min

=

77.50 mm

r

vv

=

0.00 mm

Section modulus, Z

xx

=

1760000 mm

3

Section

modulus,

Z

=

587000 mm

3

Sectional

Area,

A

=

15000 mm2

Constant,

e,

=

sqrt(275/py)

=

1 Outstand element of compression flange, b/T

=

25.78 Slender

Cl.3.5.2 and Table:7

Web

slenderness,

d/t

=

26.43 Plastic

of

BS

5950:part1

b) Design

Length

of

member,

L

=

2 m

Effective

Length

Factor

=

1 Effective

Length,

Le

=

2 m

Slenderness,

l

_{= L}

_E

_/r

_min

₌

_{25.8 OK}

_25.8

_<

₁₈₀

_Cl.

_4.7.3.2,

_BS5950

No. of fasterners at each end (IN LINE ALONG ANGLE)

=

1 Clause 4.7.10.2 Single angle struts

For struts connected to a gusset or directly to another member at each end (IN LINE ALONG ANGLE) by:

a) two or more fasterners - s lenderness

l

_{should not be less than 0.85 L/r}

vv

or 0.7L/r

aa

+ 30

(5)

Name wt/m D B t T d Ixx Iyy rxx ryy Zxx Zyy Sxx Syy u x H kN/m mm mm mm mm mm mm mm mm mm mm mm mm mm dm6 1 UC 356 x 406 x 634 6.340 474.7 424.1 47.6 77.0 290.2 2750000000 982000000 185.0 110.0 11600000 4630000 14200000 7110000 0.843 5.46 38.800 2 UC 356 x 406 x 551 5.510 455.7 418.5 42.0 67.5 290.2 2270000000 827000000 180.0 109.0 9960000 3950000 1 2100000 6060000 0.841 6.05 3 1.100 3 UC 356 x 406 x 467 4.670 436.6 412.4 35.9 58.0 290.2 1830000000 679000000 175.0 107.0 8390000 3290000 1 0000000 5040000 0.839 6.86 2 4.300 4 UC 356 x 406 x 393 3.930 419.1 407.0 30.6 49.2 290.2 1470000000 554000000 171.0 ##### 7000000 2720000 8230000 4160000 0.837 7.86 1 9.000 5 UC 356 x 406 x 340 3.400 406.4 403.0 26.5 42.9 290.2 1220000000 468000000 168.0 ##### 6030000 2320000 6990000 3540000 0.836 8.85 1 5.500 6 UC 356 x 406 x 287 2.870 393.7 399.0 22.6 36.5 290.2 1000000000 387000000 165.0 103.0 5080000 1940000 5820000 2950000 0.835 10.20 1 2.300 7 UC 356 x 406 x 235 2.350 381.0 395.0 18.5 30.2 290.2 791000000 310000000 162.0 102.0 4150000 1570000 4690000 2380000 0.834 12.10 9.540 8 UC 356 x 368 x 202 2.020 374.7 374.4 16.8 27.0 290.2 663000000 236000000 160.0 95.7 3540000 1260000 3980000 1920000 0.844 13.30 7.140 9 UC 356 x 368 x 177 1.770 368.3 372.1 14.5 23.8 290.2 572000000 205000000 159.0 95.2 3100000 1100000 3460000 1670000 0.844 15.00 6.070 10 UC 356 x 368 x 153 1.530 362.0 370.2 12.6 20.7 290.2 485000000 175000000 158.0 94.6 2680000 944000 2960000 1430000 0.844 17.00 5.090 11 UC 356 x 368 x 129 1.290 355.6 368.3 10.7 17.5 290.2 402000000 146000000 156.0 93.9 2260000 790000 2480000 1200000 0.843 19.90 4.160 12 UC 305 x 305 x 283 2.830 365.3 321.8 26.9 44.1 246.6 788000000 245000000 148.0 82.50 4310000 1530000 5100000 2340000 0.855 7.65 6.330 13 UC 305 x 305 x 240 2.400 352.6 317.9 23.0 37.7 246.6 642000000 202000000 145.0 81.40 3640000 1270000 4250000 1950000 0.854 8.73 5.010 14 UC 305 x 305 x 198 1.980 339.9 314.1 19.2 31.4 246.6 508000000 162000000 142.0 80.20 2990000 1030000 3440000 1580000 0.854 10.20 3.860 15 UC 305 x 305 x 158 1.580 327.2 310.6 15.7 25.0 246.6 387000000 125000000 139.0 78.90 2370000 806000 2680000 1230000 0.852 12.50 2.860 16 UC 305 x 305 x 137 1.370 320.5 308.7 13.8 21.7 246.6 328000000 107000000 137.0 78.20 2050000 691000 2300000 1050000 0.851 14.10 2.380 17 UC 305 x 305 x 118 1.180 314.5 306.8 11.9 18.7 246.6 276000000 90100000 136.0 77.50 1760000 587000 1950000 892000 0.851 16.20 1.970 18 UC 305 x 305 x 97 0.970 307.8 304.8 9.9 15.4 246.6 222000000 72700000 134.0 76.80 1440000 477000 1590000 723000 0.850 19.30 1.550 19 UC 254 x 254 x 167 1.670 289.1 264.5 19.2 31.7 12.7 299000000 98000000 119.0 67.90 2070000 741000 2420000 1130000 0.852 8.49 1.620 20 UC 254 x 254 x 132 1.320 276.4 261.0 15.6 25.3 12.7 226000000 75200000 116.0 66.70 1630000 576000 1870000 879000 0.850 10.30 1.180 21 UC 254 x 254 x 107 1.070 266.7 258.3 13.0 20.5 12.7 175000000 59000000 113.0 65.70 1310000 457000 1490000 695000 0.848 12.40 0.894 22 UC 254 x 254 x 89 0.890 260.4 255.9 10.5 17.3 12.7 143000000 48500000 112.0 65.20 1100000 379000 1230000 575000 0.849 14.40 0.716 23 UC 254 x 254 x 73 0.730 254.0 254.0 8.6 14.2 12.7 114000000 38700000 111.0 64.60 894000 305000 989000 462000 0.849 17.30 0.557 24 UC 203 x 203 x 86 0.860 222.3 208.8 13.0 20.5 10.2 94600000 31200000 92.7 53.20 851000 299000 979000 456000 0.850 10.20 0.317 25 UC 203 x 203 x 71 0.710 215.9 206.2 10.3 17.3 10.2 76500000 25400000 91.6 52.80 708000 246000 802000 374000 0.852 11.90 0.250 26 UC 203 x 203 x 60 0.600 209.6 205.2 9.3 14.2 10.2 60900000 20400000 89.6 51.90 581000 199000 652000 303000 0.847 14.10 0.195 27 UC 203 x 203 x 52 0.520 206.2 203.9 8.0 12.5 10.2 52600000 17700000 89.0 51.60 510000 174000 568000 264000 0.848 15.80 0.166 28 UC 203 x 203 x 46 0.460 203.2 203.2 7.3 11.0 10.2 45600000 15400000 88.1 51.10 449000 151000 497000 230000 0.846 17.70 0.142 29 UC 152 x 152 x 37 0.370 161.8 154.4 8.1 11.5 7.6 22200000 7090000 68.4 38.70 274000 91800 310000 140000 0.848 13.30 0.040 30 UC 152 x 152 x 30 0.300 157.5 152.9 6.6 9.4 7.6 17400000 5580000 67.5 38.20 221000 73100 247000 111000 0.848 16.00 0.031 31 UC 152 x 152 x 23 0.230 152.4 152.4 6.1 6.8 7.6 12600000 4030000 65.1 36.80 166000 52900 184000 80900 0.837 20.40 0.021 32 UB 305 x 102 x 28 0.280 308.9 101.9 6.1 8.9 275.9 54200000 1570000 122.0 20.80 351000 30800 407000 48900 0.858 37.00 0.035 33 UB 305 x 102 x 33 0.330 312.7 102.4 6.6 10.8 275.9 64900000 1930000 125.0 21.50 415000 37800 480000 59800 0.866 31.70 0.044 34 UB 305 x 127 x 42 0.420 306.6 124.3 8.0 12.1 264.6 81400000 3880000 124.0 27.00 531000 62500 610000 98200 0.872 26.50 0.084 35 UB 305 x 127 x 48 0.480 310.4 125.2 8.9 14.0 264.6 95000000 460000 125.0 27.50 612000 73500 706000 116000 0.874 23.30 0.101 36 UB 305 x 165 x 40 0.400 303.8 165.1 6.1 10.2 265.7 85200000 7630000 129.0 38.50 561000 924000 624000 141000 0.888 31.10 0.164 37 UB 305 x 165 x 54 0.540 310.9 166.8 7.7 13.7 265.7 117000000 10600000 131.0 39.40 753000 127000 845000 195000 0.890 23.70 0.234 38 UB 350 x 169 x 45 0.450 350.0 169.0 4.9 7.7 312.3 91545600 6197690 145.4 33.00 523118 73345 589364 113492 0.900 45.45 39 UB 354x169x51 0.510 353.6 169.5 5.3 9.5 312.3 UB 305 x 127 UB 305 x 12 #VALUE! ##### #VALUE! #VALUE! #VALUE! #VALUE! 0.900 37.22

(6)

40 UB 356 x 171 x 45 0.450 352.0 171.0 6.9 9.7 312.3 121000000 8120000 146.0 37.80 687000 95000 774000 147000 0.875 36.90 0.238 41 UB 356 x 171 x 57 0.570 358.6 172.1 8.0 13.0 312.3 161000000 11100000 149.0 39.20 896000 129000 1010000 199000 0.884 28.90 0.331 42 UB 356 x 171 x 67 0.670 364.0 173.2 9.1 15.7 312.3 195000000 13600000 151.0 39.90 1070000 157000 1210000 243000 0.887 24.40 0.413 43 UB 356 x 368 x 129 1.290 355.6 368.3 10.7 17.5 290.2 402000000 146000000 156.0 93.90 2260000 790000 2480000 1200000 0.843 19.90 4.160 44 UB 406 x 140 x 39 0.390 397.3 141.8 6.3 8.6 359.7 125000000 4110000 159.0 28.90 627000 58000 721000 91100 0.859 38.80 0.155 45 UB 406 x 140 x 46 0.460 402.3 142.4 6.9 11.2 359.7 156000000 5390000 163.0 30.20 778000 75700 888000 118000 0.870 47.40 0.206 46 UB 459 x 191 x 67 0.670 453.6 189.9 8.5 12.7 407.9 294000000 14500000 185.0 41.20 1300000 153000 1470000 237000 0.873 37.90 0.706 47 UB 533 x 210 x 82 0.820 528.3 208.7 9.6 13.2 476.5 475000000 20100000 213.0 43.80 1800000 192000 2060000 300000 0.865 41.60 1.330 48 UB 533 x 210 x 101 1.014 536.7 210.1 10.9 17.4 476.5 617000000 26900000 218.0 45.60 2300000 257000 2620000 400000 0.874 33.10 1.820 49 UB 533 x 210 x 82 0.820 528.3 208.7 9.6 13.2 476.5 475000000 20100000 213.0 43.80 1800000 192000 2060000 300000 0.865 41.60 1.330 50 UB 533 x 210 x 101 1.014 536.7 210.1 10.9 17.4 476.5 617000000 26900000 218.0 45.60 2300000 257000 2620000 400000 0.874 33.10 1.820 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 A 5083 111900000 1.215 1.534 7714630 124693 1874 3221 0

(7)

J Area b rvv mm mm mm mm ######### 80800 211.8 ######### 70200 209.3 ######### 59500 206.5 ######### 50100 203.7 ######### 43300 201.6 ######### 36600 199.7 8120000.0 30000 197.5 5600000.0 25800 187.1 5830000.0 22600 186.1 2510000.0 19500 185.1 1530000.0 16500 183.8 ######### 36000 161.0 ######### 30600 159.1 7340000.0 25200 157.0 3790000.0 20100 155.3 2500000.0 17500 154.3 1600000.0 15000 153.3 911000.0 12300 152.5 6250000.0 21200 132.2 3220000.0 16900 130.5 1730000.0 13700 129.2 1040000.0 11400 128.0 573000.0 9290 126.9 1380000.0 11000 104.3 815000.0 9110 103.1 466000.0 7580 102.7 320000.0 6640 102.0 222000.0 5880 101.6 195000.0 4740 77.2 105000.0 3820 76.4 48700.0 2980 76.2 76300.0 3630 50.9 121000.0 4180 51.2 210000.0 5320 62.2 314000.0 6080 62.6 147000.0 5200 82.5 345000.0 6840 83.4 74654.3 4330 84.5 UB 305 x 1 5083 84.8

(8)

157000.0 5700 85.5 331000.0 7220 86.1 555000.0 8540 86.7 1530000.0 16500 183.8 106000.0 4940 70.9 192000.0 5900 71.2 371000.0 8500 95.0 513000.0 10400 104.4 1020000.0 12900 105.1 513000.0 10400 104.4 1020000.0 12900 105.1 19 20 21 22