Download xls - Design Beam

1

BS8110 REF. CALCULATION OUTPUT

I/ Design BeamGB9A effective span= 7.7 m

1 -Loading Slab Panel 7.7 x 2.3 m and 0.1 mTHK (Slab on one side of the beam)

Dead Load

Slab 24 kN/m³ x 2.08 m³ / 7.7 = 6.48 kN/m

Beam 25 kN/m³ x 1.05 m³ / 7.7 = 3.4 kN/m

Other 1 kN/m² x 2.25 m = 2.25 kN/m

Wall 10cm 1.2 kN/m² x 2.25 m = 2.7 kN/m

Wall 20cm 0 kN/m² x 0 m = 0 kN/m

Floor Finis 1.5 kN/m² x 2.25 m = 3.38 kN/m

Total Dead Lo ### kN/m (Trapezoidal Dead load per m lenght

Live Load or Imposed load on one side of the beam)

Floor LL 4 kN/m² x 2.25 m³ / m = 9 kN/m

Total live Load 9 kN/m (Trapezoidal Live load per m lenght

Design Load on one side of the beam)

Design Load1.6 x ### )+( 1.4 x 9.00 ) = 42 kN/m (Trapezoidal load= 41.73 kN/m)

Convert Trapezoidal load to uniformly distributed load

Uniformly distributed ### x 0.73 ) = 30 kN/m

Load on the other side of th 30 - ( ### x 30 / 100 )= 21 kN/m (Reduce 30% for the load on

the other side)

Total Load on both side of t 30 + ### = ### kN/m

2 -Bending Moment

Max moment at suppo = - ql²/12 = ### kN/m

Max moment at mid s = ql²/24 = ### kN/m

Msup

Mmid

2

3 -Beam Section

h=L

toL

=7700

to7700

» h= 550 mm » h= 400 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5400 » b= 248 mm » b= 200 mm

Cover: C= 25 mm 6 mm ; 20 mm

d= = 400 - 25 - 3 - 10 = 362 mm » d'= 35 mm

ii -Define Steel Area

Assume fcu= 30 N/mm² ; fy v= 250 N/mm² fy = 390 N/mm²

a -Define Steel Area at Support Mmax= 255.89 kNm

k=M

=256 x

0.325 > 0.156200 x 131044 x 30

z =d.[0.5+(0.25-(k'/0.9))^(1/ 2)]=362.[0.5+(0.25-(0.132/ 0.9)^(1/ 2))]= 297 mm

that z not exceed 0.95d= 344 mm so z = 344 mm

» [(k'. fcu.b.d^2)/(0.87.fy.z)]+ = [(0.13x30x200x362^2)x10^6) / (0.87x390x343.

3087.5 » Assume 11 T 20 » ###

» P=100(As,req / bd) 4.32 > 0.13 < 4 » OK

b -Define Steel Area at Mid span Mmax= 160 kNm

k=M

=160 x

0.203 > 0.156200 x 131044 x 30

z =d.[0.5+(0.25-(k'/0.9))^(1/ 2)]=.[0.5+(0.25-(0.132/ 0.9)^(1/ 2))]= 297 mm


» [(k'. fcu.b.d^2)/(0.87.fy.z)]+ = [(0.13x30x200x362^2) x10^6)/ (0.87x3

2285.9 » Assume 9 T 20 » ###

;Assume Steel Bar ØDR= DT=

h - C - DR/2 - DT/2

106 (Doubly Reinforced

Section)bd2fcu

As =

As = mm2 As= mm2

106 (Doubly Reinforced

Section)bd2fcu

As =

As = mm2 As= mm2

3

» P=100(As,req / bd) 3.53 > 0.13 < 4 » OK

c -Check Deflection

=160 x

= 6.10200 x 1E+05

fs =5

fy =5

x 390 x###

= 197 (Service Stress)8 8 ###

modification factor = 0.55 +477 - fs

= 1120

Bassic span/depth = 26 ( table3.9 in Code BS8110 Part 1 1985)

Allowable span/depth= 26 x 1 = 25

Actual span/depth = lx / dx = ### / 362 = 21

» »Allowable span/depth= 25 >Actual span/depth= 21 » OK

c -Link

Max Shear at Support

= 168 kN

= / bd = 168x(10^3) / 200x362= 2.32 N/mm²

= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.63 x [((100x2826)/(200x362))^(1/3)]x(400/362)^(1/4)x(30/25)^(1/3)

= 1.08

= 2.32 N/mm² > +0.4=1.48 N/mm² (Case 3 in table3.7 in Code BS8110)

Assume 6 mm » Area of link Asv= 55

» Link Spacin = 48 mm » 80 mm

Hence R6@80

Shear at L/4 from the support

= 150 kN

Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

Vmax

Vstress Vmax

Vcapacity

Vstress Vcapacity

Asv≥(bv Sv(vs-vc))/0.87fy mm2

Sv≤(Asv x 0.87fy)/(bv(vs-vc))

Vl/4

4

= 2.07 N/mm²

= 1.08 N/mm² Assume 6 mm » Area of link Asv= 55


Hence R6@180

Vstress

Vcap. mm2


5

RE-Design Section of Ground GB9A


I/ Design BeamGB9A effective span= 5 m

1 -Loading Slab Panel 5 x 2.5 m and 5 x 2.5 m and 0.1 mTHK

Dead Load

Left Side of the beam Right Side of the beam

Slab 24 kN/m³ x 0.12 x 2.5 = 7.2 kN/m 24 kN/m³ x 0.12 x 2.5 = 7.2 kN/m

Beam 24 kN/m³ x 0.35 x 0.2 = 1.68 kN/m

Other 0 kN/m²x 2.5 = 0 kN/m 0 kN/m²x 2.5 = 0 kN/m

Wall 10cm 1.2 kN/m²x 3.3 = 3.96 kN/m 1.2 kN/m²x 3.3 = 3.96 kN/m

Wall 20cm 0 kN/m²x 0 = 0 kN/m 0 kN/m²x 0 = 0 kN/m

Floor Finish 1.5 kN/m²x 3.3 = 4.95 kN/m 1.5 kN/m²x 3.3 = 4.95 kN/m

Total Dead Load ### kN/m ### kN/m

Live Load or Imposed load

Floor LL 1.5 kN/m² x 2.5 m = 3.75 kN/m 1.5 kN/m² x 2.5 m = 3.75 kN/m

Total live Load 3.8 kN/m 3.8 kN/m

Triangle or Trapezoidal Design Load

(1.4 x 17.79) + (1.6 x 3.75) = ### kN/m (1.4 x 16.11) + (1.6 x 3. = ### kN/m

Convert Trapezoidal load to uniformly distributed load for bending moment

Uniformly distributed 30.9 x 0.7 = 21 kN/m 28.6 x 0.7 = 19 kN/m

Total uniformly distributed load

20.6 + 19 = 39 kN/m

6


2 -Bending Moment

Max moment at suppo = - ql²/12 = -82.14 kN/m

Max moment at mid s = ql²/24 = 41.07 kN/m

3 -Beam Section

h=L

toL

=5000

to5000

» h= 357 mm » h= 350 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5350 » b= 161 mm » b= 200 mm


d= = 350 - 25 - 3 - 8 = 314 mm d'= 33 mm

4 -Define Steel Area



k=M

=82 x

0.139 < 0.156200 x 98596 x 30

z = d.[0.5+(0.25-(k/0.9))^(1/ 2)]=314.[0.5+(0.25-(0.139/ 0.9)^(1/ 2))]= 254 mm


x = ( 314 - 298 )/ 0.45 = 34.89

» Compression Steel Area

» No Steel Require

» Tension Steel Area

» M /0.87 fy.z = [(82x10^6) / (0.87x390x298.3)]

811.59 » Assume 5 T 16 » ###

» P=100(As,req / bd) 1.44 > 0.13 < 4 » OK

Msup

Mmid

;Assume Steel Bar ØDR= DT=

h - C - DR/2 - DT/2

106 (Singly Rienforced

Section)bd2fcu

As =

As = mm2 As= mm2

7


b -Define Steel Area at Mid sp Mmax= 41.07 kNm

k=M

=41 x

0.069 < 0.156200 x 98596 x 30

z = d.[0.5+(0.25-(k/0.9))^(1/ 2)]=.[0.5+(0.25-(0.069/ 0.9)^(1/ 2))]= 288 mm


x = ( 0 - 298 )/ 0.45 = -663


» No Steel Require


» M /0.87 fy.z = [(41x10^6) / (0.87x390x298.3)]

405.8 » Assume 3 T 16 603

» P=100(As,req / bd) 0.96 > 0.13 < 4 » OK

c -Check Deflection

=41.1 x

= 2.08200 x 98596

fs =5

fy =5

x 390 x406

= 164 (Service Stress)8 8 603


= 1.94120


Allowable span/depth= 26 x 1.94 = 50

Actual span/depth = lx / dx = ### / 314 = 16

» »Allowable span/depth= 50 >Actual span/depth= 16 » OK

106 (Singly Rienforced

Section)bd2fcu

As =

As = mm2 As= mm2

Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

8


d -Link



Uniformly distributed 30.9 x 0.5 = 15 kN/m 28.6 x 0.5 = 14 kN/m


15.5 + 14 = 30 kN/m Total load per m lenght for

bending moment 29.7 kN/m


= ql/2 = 74 kN

= / bd = 1.18 N/mm²

= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.83 N/mm²

= 1.18 N/mm² > +0.4=1.23 N/mm²(Case 3 in table3.7 in Code BS8110)

Assume 6 mm » Area of link Asv= 55


Hence R6@120

Shear at L/4 from the support

= q(l-0.25l)/2 = 55.7 kN

= 0.89 N/mm²

= 0.83 N/mm² Assume 6 mm » Area of link Asv= 55

» Link Spacin = ### mm » 150 mm

Hence R6@150

Vmax

Vstress Vmax

Vcapacity

Vstress Vcapacity

mm2


Vl/4

Vstress

Vcap. mm2


9

Check Existing Section of Ground Beam GB7 (Along Grid 4 from Grid E-G)


I/ Check ExistiGB7 effective span= 6.6 m

A Loading Slab Panel 6.6 x 3.3 m and 6.6 x 1.1 m and 0.1 mTHK

Dead Load



Beam 24 kN/m³ x 0.2 x 0.4 = 1.92 kN/m

Roof Load 0 kN/m²x 1.7 = 0 kN/m 0 kN/m²x 0.83 = 0 kN/m




Total Dead Load ### kN/m 8.3 kN/m


Floor LL 4 kN/m² x 3.3 m = 13.2 kN/m 4 kN/m² x 1.1 m = 4.4 kN/m

Roof LL 0 kN/m² x 1.7 m = 0 kN/m 0 kN/m² x 0.83 m = 0 kN/m

Total live Load 13 kN/m 4.4 kN/m


(1.4 x 18.75) + (1.6 x 13.2) = ### kN/m (1.4 x 8.25) + (1.6 x 4.4) = ### kN/m


Uniformly distributed 47.4 x 1 = 47 kN/m 18.6 x 1 = 19 kN/m


47.4 + 18.6 = 65.96 kN/m

10


B Bending Moment



C -Beam Section

h=L

toL

=6600

to6600

» h= 471.43 mm » h= 400 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5)400 » b= 212.14 mm » b= 200 mm


d= = 400 - 25 - 4 - 10 = 361 mm d'= 35 mm

D-Define Steel Area




Existing Steel Area 2 T 20 » 628


Existing Steel Area 4 T 20 » ### 0 T 25 » 0

Total Steel Area 1884 mm²

» P=100(As,req / bd) 2.36 > 0.13 < 4 » OK

b -Define Steel Area at Mid spanMmax= 119.72 kNm




Existing Steel Area 4 T 20 » ###


» P=100(As,req / bd) 2.36 > 0.13 < 4 » OK

Msup

Mmid

;Assume Steel Bar Ø DR= DT=

h - C - DR/2 - DT/2

As'= mm2

As= mm2 As'= mm2

As'= mm2

As= mm2

11


c -Link or Stirrup





47.4 + 18.6 = 65.96 kN/m


= ql/2 = 218 kN

= / bd = 3.01 N/mm²

Max Shear Stress = 4.38 N/mm²

= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.95 N/mm²

+0.4= 1.35 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))

6 mm » Area of link Asv= 57


Hence R6@30

» Existing Link Ø 6 mm @ 150 mm not enough

Vmax

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity

Asv≥(bv Sv(vs-vc))/0.87fy Assume ø mm2


12


Shear at L/4

= = 163 kN

= / bd = 2.26 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.95 N/mm²

+0.4= 1.35 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R6@50


d -Check Deflection

=120 x

= 4.59200 x 130321

fs =5

fy =2

x 390 x1884



= 1120


Allowable span/dep = 26 x 0.987 = 25.674

Actual span/depth = l /### = 6600 / 250 = 26.4 mm

Vmax qll/4 / 2

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity

Asv≥(bv Sv(vs-vc))/0.87fy Assume Ø mm2


Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

13

» »Allowable span/depth= 25.67 <Actual span/depth= 26 » NO


e -Check Cracking

Refer 3.12.11.2.3

1/ CLear distance between horizontal tension bars

Allowable clear distance between bars

= 155 (table 3.28)

=

= 47 mm < 155 OK

Clear Distance between the face of the beam and nearest longitudinal bar in tension

=

y =

= 43 mm

Allowable distance

= 155x0.5 = 77.5 mm

» = 50.81 mm < 77.5 bar should be provided in side faces of beam to control cracking

Distance between bars

S1 (b-2(cover)-2(Ølinks)-2(Øbar))/2

S2 ((y2+y2)^(1/2))-(Øbar/2)

cover+Ølink+(Øbar/2)

S2

14

Sb ≤ 250 mm

Minimum size bar

Ø >

> 11.32 mm Provide DB12 @ 250

((Sbb/fy)^(1/2))

15

Check Existing Section of Ground Beam GB9 (Along Grid E from Grid 7'-9')


I/ Check ExistiGB9 effective span= 7.7 m


Dead Load



Beam 24 kN/m³ x 0.2 x 0.4 = 1.92 kN/m











(1.4 x 14.46) + (1.6 x 8.8) = ### kN/m (1.4 x 10.4) + (1.6 x 6.6) = ### kN/m




34.3 + 25.1 = 59.44 kN/m

16


B Bending Moment



C -Beam Section

h=L

toL

=7700

to7700

» h= 550 mm » h= 400 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5)400 » b= 247.5 mm » b= 200 mm


d= = 400 - 25 - 4 - 10 = 361 mm d'= 35 mm

D-Define Steel Area






Existing Steel Area 2 T 20 » 628 3 T 25 » ###


» P=100(As,req / bd) 3.85 > 0.13 < 4 » OK







Msup

Mmid


h - C - DR/2 - DT/2

As'= mm2

As= mm2 As'= mm2

As'= mm2

As= mm2

17

» P=100(As,req / bd) 4.46 > 0.13 < 4 » OK


c -Link or Stirrup





34.3 + 25.1 = 59.44 kN/m


= ql/2 = 229 kN

= / bd = 3.17 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 1.11 N/mm²

+0.4= 1.51 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R6@30


Vmax

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



18


Shear at L/4

= = 172 kN

= / bd = 2.38 N/mm²

Max Shear Stress = 2 N/mm²

= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 1.11 N/mm²

+0.4= 1.51 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R6@50


d -Check Deflection

=147 x

= 5.63200 x 130321

fs =5

fy =2

x 390 x3572

= 260 (Service Stress)8 3 3571.8


= 0.91120


Vmax qll/4 / 2

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

19





e -Check Cracking

Refer 3.12.11.2.3



= 155 (table 3.28)

=

= 42 mm < 155 OK


=

y =

= 45.5 mm

Allowable distance

= 155x0.5 = 77.5 mm




S2 ((y2+y2)^(1/2))-(Øbar/2)


S2

20

Sb ≤ 250 mm

Minimum size bar Ø >

> 11.323 mm

Provide DB12 @ 250

((Sbb/fy)^(1/2))

21

Check Existing Section of First Floor Beam B2a (Along Grid E from Grid 7'-9')


I/ Check ExistiB2a effective span= 7.7 m


Dead Load



Beam 24 kN/m³ x 0.25 x 0.6 = 3.6 kN/m











(1.4 x 17.2) + (1.6 x 8.8) = ### kN/m (1.4 x 11.19) + (1.6 x 6.6) = ### kN/m




38.2 + 26.2 = 64.38 kN/m

22


B Bending Moment



C -Beam Section

h=L

toL

=7700

to7700

» h= 550 mm » h= 600 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5)600 » b= 247.5 mm » b= 250 mm


d= = 600 - 25 - 4 - 10 = 561 mm d'= 35 mm

D-Define Steel Area








» P=100(As,req / bd) 2.05 > 0.13 < 4 » OK







Msup

Mmid


h - C - DR/2 - DT/2

As'= mm2

As= mm2 As'= mm2

As'= mm2

As= mm2

23

» P=100(As,req / bd) 2.38 > 0.13 < 4 » OK


c -Link or Stirrup





38.2 + 26.2 = 64.38 kN/m


= ql/2 = 248 kN

= / bd = 1.77 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.80 N/mm²

+0.4= 1.20 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@90


Vmax

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



24

Shear at L/4

= = 186 kN

= / bd = 1.33 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.80 N/mm²

+0.4= 1.20 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@160

» Existing Link Ø 8 mm @ 125 mm safe enough

d -Check Deflection

=159 x

= 2.02250 x 314721

fs =5

fy =2

x 390 x3572



= 1.54120




» »Allowable span/depth= 40.15 >Actual span/depth= 31 » OK

Vmax qll/4 / 2

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

25

e -Check Cracking

Refer 3.12.11.2.3



= 155 (table 3.28)

=

= 67 mm < 155 OK


=

y =

= 45.5 mm

Allowable distance

= 155x0.5 = 77.5 mm



Sb ≤ 250 mm


S2 ((y2+y2)^(1/2))-(Øbar/2)


S2

26

Minimum size bar

Ø >

> 12.66 mm

Provide DB12 @ 250

((Sbb/fy)^(1/2))

27

Check Existing Section of Roof Floor Beam RB1A (Along Grid H from Grid 2-4)


I/ Check ExistiRB1A effective span= 6.6 m


Dead Load



Beam 24 kN/m³ x 0.2 x 0.4 = 1.92 kN/m

Roof Load 1.5 kN/m²x 1.7 = 2.55 kN/m 1.5 kN/m²x 0.83 = 1.24 kN/m

Wall 10cm 0 kN/m²x 3.3 = 0 kN/m 0 kN/m²x 3.3 = 0 kN/m






Roof LL 1.5 kN/m² x 1.7 m = 2.55 kN/m 1.5 kN/m² x 0.83 m = 1.24 kN/m

Total live Load 5 kN/m 3.7 kN/m


(1.4 x 11.7) + (1.6 x 5.03) = ### kN/m (1.4 x 8.47) + (1.6 x 3.72) = ### kN/m




24.4 + 17.8 = 42.23 kN/m

28


B Bending Moment



C -Beam Section

h=L

toL

=6600

to6600

» h= 471.43 mm » h= 400 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5)400 » b= 212.14 mm » b= 200 mm


d= = 400 - 25 - 4 - 10 = 361 mm d'= 35 mm

D-Define Steel Area






Existing Steel Area 2 T 20 » 628 2 T 16 » 402


» P=100(As,req / bd) 2.07 > 0.13 < 4 » OK







Msup

Mmid


h - C - DR/2 - DT/2

As'= mm2

As= mm2 As'= mm2

As'= mm2

As= mm2

29

» P=100(As,req / bd) 2.36 > 0.13 < 4 » OK


c -Link or Stirrup





24.4 + 17.8 = 42.23 kN/m


= ql/2 = 139 kN

= / bd = 1.93 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.91 N/mm²

+0.4= 1.31 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@100


Vmax

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



30

Shear at L/4

= = 105 kN

= / bd = 1.45 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.91 N/mm²

+0.4= 1.31 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@200


d -Check Deflection

=76.6 x

= 2.94200 x 130321

fs =5

fy =2

x 390 x1884



= 1.23120




» »Allowable span/depth= 32.07 >Actual span/depth= 26 » OK

Vmax qll/4 / 2

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

31

e -Check Cracking

Refer 3.12.11.2.3 BS8110



= 155 (table 3.28)

=

= 47 mm < 155 OK


=

y =

= 43 mm

Allowable distance

= 155x0.5 = 77.5 mm



Sb ≤ 250 mm


S2 ((y2+y2)^(1/2))-(Øbar/2)


S2

32

Minimum size bar

Ø >

> 11.32 mm

Provide DB12 @ 250

((Sbb/fy)^(1/2))

33

Check Existing Section of Roof Floor Beam RB15B (Along Grid E from Grid 1-5)


I/ Check ExistiRB15B effective span= 9.9 m


Dead Load



Beam 24 kN/m³ x 0.25 x 0.6 = 3.6 kN/m

Roof Load 1.5 kN/m²x 1.7 = 2.55 kN/m 1.5 kN/m²x 0.83 = 1.24 kN/m







Roof LL 1.5 kN/m² x 1.7 m = 2.55 kN/m 1.5 kN/m² x 0.83 m = 1.24 kN/m



(1.4 x 15.79) + (1.6 x 5.85) = ### kN/m (1.4 x 8.47) + (1.6 x 3.72) = ### kN/m




31.5 + 17.8 = 49.27 kN/m

34


B Bending Moment



C -Beam Section

h=L

toL

=9900

to9900

» h= 707.14 mm » h= 600 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5)600 » b= 318.21 mm » b= 250 mm


d= = 600 - 25 - 4 - 10 = 561 mm d'= 35 mm

D-Define Steel Area








» P=100(As,req / bd) 2.05 > 0.13 < 4 » OK







Msup

Mmid


h - C - DR/2 - DT/2

As'= mm2

As= mm2 As'= mm2

As'= mm2

As= mm2

35

» P=100(As,req / bd) 2.38 > 0.13 < 4 » OK


c -Link or Stirrup





31.5 + 17.8 = 49.27 kN/m


= ql/2 = 244 kN

= / bd = 1.74 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.80 N/mm²

+0.4= 1.20 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@90


Vmax

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



36

Shear at L/4

= = 183 kN

= / bd = 1.3 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 0.80 N/mm²

+0.4= 1.20 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@170


d -Check Deflection

=201 x

= 2.56250 x 314721

fs =5

fy =2

x 390 x3572



= 1.34120





Vmax qll/4 / 2

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

37

e -Check Cracking

Refer 3.12.11.2.3



= 155 (table 3.28)

=

= 67 mm < 155 OK


=

y =

= 45.5 mm

Allowable distance

= 155x0.5 = 77.5 mm



Sb ≤ 250 mm


S2 ((y2+y2)^(1/2))-(Øbar/2)


S2

38

Minimum size bar

Ø >

> 12.66 mm

Provide DB12 @ 250

((Sbb/fy)^(1/2))

39

Check Existing Section of First Floor Beam B1 (Along Grid G from Grid 13-15)


I/ Check ExistiB1 effective span= 6.6 m

A Loading Slab Panel 6.6 x 2.2 m and 6.6 x 0 m and 0.1 mTHK

Dead Load


Slab 24 kN/m³ x 0.12 x 2.2 = 6.34 kN/m 24 kN/m³ x 0.12 x 0 = 0 kN/m

Beam 24 kN/m³ x 0.2 x 0.3 = 1.44 kN/m



Wall 20cm 2.3 kN/m²x 4.3 = 9.89 kN/m 2.3 kN/m²x 0 = 0 kN/m

Floor Finish 1.5 kN/m²x 2.2 = 3.3 kN/m 1.5 kN/m²x 0 = 0 kN/m



Floor LL 4 kN/m² x 2.2 m = 8.8 kN/m 4 kN/m² x 0 m = 0 kN/m


Total live Load 8.8 kN/m 0 kN/m


(1.4 x 20.97) + (1.6 x 8.8) = ### kN/m (1.4 x 0) + (1.6 x 0) = 0.0 kN/m




43.4 + 0 = 43.43 kN/m

40


B Bending Moment



C -Beam Section

h=L

toL

=6600

to6600

» h= 471.43 mm » h= 300 mm10 15 10 15

b=(0.4 to 0.5)h= (0.4 to 0.5)300 » b= 212.14 mm » b= 200 mm


d= = 300 - 25 - 4 - 10 = 261 mm d'= 35 mm

D-Define Steel Area






Existing Steel Area 4 T 20 » ### 0 T 25 » 0


» P=100(As,req / bd) 2.76 > 0.13 < 4 » OK







Msup

Mmid


h - C - DR/2 - DT/2

As'= mm2

As= mm2 As'= mm2

As'= mm2

As= mm2

41

» P=100(As,req / bd) 2.05 > 0.13 < 4 » OK


c -Link or Stirrup





43.4 + 0 = 43.43 kN/m


= ql/2 = 143 kN

= / bd = 2.75 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 1.09 N/mm²

+0.4= 1.49 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@70


Vmax

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



42

Shear at L/4

= = 107 kN

= / bd = 2.06 N/mm²


= (0.79/1.25) [(100As/bd)^(1/3)] [(400/d)^(1/4)] [(fcu/25)^(1/3)]

= 1.09 N/mm²

+0.4= 1.49 N/mm²

» Vc+0.4 Vs < 0.8(fcu^(1/2))



Hence R8@100


d -Check Deflection

=78.8 x

= 5.79200 x 68121

fs =5

fy =2

x 390 x1231



= 0.9120





Vmax qll/4 / 2

Vstress Vmax

0.8(fcu^(1/2))

Vcapacity

Vcapacity



Mmax 106

bd2

As,req

As,pro

(0.9+(M / bd2))

43

e -Check Cracking

Refer 3.12.11.2.3



= 155 (table 3.28)

=

= 51 mm < 155 OK


=

y =

= 41 mm

Allowable distance

= 155x0.5 = 77.5 mm

» = 50 mm < 77.5 bar should be provided in side faces of beam to control cracking


Sb ≤ 250 mm


S2 ((y2+y2)^(1/2))-(Øbar/2)


S2

44

Minimum size bar

Ø >

> 11.32 mm

Provide DB12 @ 250

((Sbb/fy)^(1/2))