Lintel++beam+(when+height+less+) 4t343u



Lintel are provided over the opning of door, window, almirah, etc. Generally, they the load of the wall over it, and some times also the live load are transferred by the sub - roof of the room. Following five cases may arise from point of view of distribution of load over the Lintel :1 2 3 4 5

When the length of wall on each side is more than half the effective span of the lintel. When the length of wall to one side is less than half the effective span of the lintel. When the length of wall on both side is less than half the effective span of the lintel. When there are opening over lintel When there is load carrying slab over the lintel. Case 1:- When the length of wall on each side is more than half the effective span of the lintel. The most general case.Because of arch-action in the masonry, all the load of wall above the lintel is not transferred to the lintel.It ia assumed that the load transferred is in the form of H triangle,and the load on the lintel is equal to the weight of the masonry in triangular portion, as h shown in fig 1. If, however, the height of the wall above the lintel is insufficient (i.e.if apex of triangle falls above the top of wall), whole of the rectangulare load above the lintelis taken to act on lintel, as shown in fig 2 >L/2 l >L/2 0 Case 1 (H>Lsin 60 ) H = height of wall above the lintel. L = Effective span L = Effective length of opening. l = Actual opening. Fig 1 h = Effective height of masonry. Thus, h = Lsin 60 0 = L x3/2 or L/2 x  Tringle area = 1/2 x L x L/2 3

2

h

H

>L/2 l >L/2 Case 1 (H
Case 2:- When the length of wall one side is less than half the effective span of the lintel. Fig 2 show the situation where the length of wall to one side is less than the half the effective span, but the length to the other side is more than the half the effective span. In case, the load transferred to the lintel will be equal to the weight of masonry contained in the rectangle of height h equal to effective span.

h=L

H 60 0

60 0

L/2 Case 2 (H
3 Case 3:- When the length of wall each side is less than half the effective span of the lintel. H=h This shown in Fig 3. The load acting on lintel will be equal to the weight of masonry contained in rectangule of height h equal to the full height H of wall.

60 0

60 0


60 0

60 0

60 0

60 0

60 0

60 0 L

5 Case 5:- When there is load carrying slab falling with in dispression triangle. If the roof slab is provided at a level well above the apex of the dispresion triangl, uniformly distributed load carriied by slab is not, transferred to lintel.If, however, the slab intersects the dispresion triangle, three type of loads are transferred to the lintel :

Case 4

Fig 5

h2 = Lsin 60 0 w3 slab

1. Load W1 due the weight of masonry contained in rectangle of height h1 equal to the height of slab above the lintel. 2. Load W2 carried by slab, in alength L. 3. Load W3 due to weight of masonry contained in equilateral triangle above the slab. The design of lintel is similar to that R.C. beam discussed in beam . The width of lintel is normally kept equal to width of wall. The maximum

w2

h1

w1

L \

Total M=

Wl

x

wL2

6 8 The maximum shear will act at the edge of opening and is given by W + wll F= 2 2

Case 5

Fig 6

Design of Lintel beam (H
pkn

Clear Span (opening ) Wall width Room size Slab thickness Lime tarrace Thickness Super imposed load Height of masonry above lintel Conrete Steel

Mfy

scbc

10 Nominal Cover 11 Reinforcement Main Bottom Anchor bars (top ) Strirrups

2.00 0.30 5.00 16 10 1.6 1.50 20 415 7 25 12 8 8

mm mm

x cm cm kN / m2 mtr

Unit wt. of masonry wt. of concrete Tensile stress m

N/mm2 N/mm2 mm

Effective Cover

mmF mmF mmF

4 2 210

8 mm f 2 lgdstrips 210 mm c/c 210

18.00 0.16 0.10

mtr mtr mtr

19.00 24.00 230 13.3 30

kN / m3 kN / m3 N/mm2 mm

Nos. Nos. mm c/c

2000 mm

300 250

2000 300

mtr mtr

300 8 mm F 2 nos anchor bars 210 250 mm

300

300 4 nos bars (a) L section

12

mmF

mmF top anchor bars 2 nos bars 8 mmF 2 nos bars 12 mmf 2 lgdstrips 210 mm c/c mmF 4 nos bars 12 mmF 2 nos bars 12

25 mm cover

8 250 mm

200 mm (b) section at mid span [email protected]

200 © section at mm

200 mm

25 mm cover

Design of Lintel Beam (when height is less) Clear Span (opening ) Wall width Room size Slab thickness Lime tarrace thickness Super imposed load Height of masonry above lintel #REF! M20 fy 415 Nominal cover Effective cover

2.00 0.30 5.00 16.00 10.00 1.60 1.50 19.00

mtr mtr or 300 mm x 18.00 mtr cm or 0.16 mtr cm or 0.10 mtr 2 2 kN / m 1600 N/m mtr 3 kN / m3 or 19000 N/m 3 wt. of concrete 24 kN/m 2 2 N/mm Tensile stess = 230 kN/m 25 mm 30 mm

1 Design Constants:- For HYSD Bars

sst = scbc = m

Cocrete M =

= 230 N/mm2 N/mm3 = 7 = 13.33 k=

m*c

m*c+sst j=1-k/3 = 1 R=1/2xc x j x k = 0.5

20

wt. of concrete

2 = 25000 N/mm

= 0.289

=

13.33 13.33 x

x 7

-

0.289

/

3

x

7

x

0.904

7 +

3 or 24000 N/M

230

= 0.904 x 0.289 =

0.9130

2 Caculcation of B.M. :Let effective depth of beam = span /10= 2 / 8 = 0.25 mtr cover = 0.025 mtr Assume Total depth of Beam = 0.25 +2 x cover = 0.25 + 2 x 0.03 = 0.30 mtr Let width of Beam = width of wall = 0.30 mtr 300 mm self Load of Beam per meter run = 0.30 x 0.30 x 1 x #### = 2160 N/m Effective span will be the minimum of following. 1 Center to center of bearing : Providing a bearing of 0.30 mtr L= 2.00 + 0.30 = 2.30 mtr 0 60dispresion Heigh of equtlateral triangle, assuming L 2.30 = x = = 2.00 m 3 x 3 Lsin 60 0 2.00 2 Height of masonry above lintel 1.50 mtr This is > than the height of of the masonry above lintel. Hence load of the slab will also transferred to lintel . fig show the elevation, showing all the height. If we construct equilateral triangle above the top of slab. Its apex will fall very much above the top of the parapet wall. Hence the weight of whole wall above the lintel will transferred to the lintel. thus the load per mtr length of lintel will connist of the follwing. (1) weight of wall :weight per meter run.= 2.16 x #### = 12312 N 0.30 x 1 (2) Live load on strip = x 5.00 x 1.00 x 1600 = 4000 N 2 1 (3) Dead weight of slab = x 5.00 x 1.00 x 0.16 x 24000 = 9600 N 2 Dead weight of Lime 1 (4) = x 5.00 x 1.00 x 0.10 x 19000 = 4750 N concrete 2 Total load per meter run of lintel = 18350 N \ Self weight of lintel (5) = 0.30 x 0.30 x 1 x 24000 = 2160 N weight per meter run Total weight = 12312 + #### + 2160 '= 32822 N 2 x 32822 x 2.30 2.3 wL Max. possible Bending moment = = = 21704 N-m 8 8 3 6 [email protected] or 21704 x 10 N-mm or 21.704 x 10 N-mm

2 Design of setion :Effective depth required

=

Let us take d

=

BM Rxb

=

10 3

21704 x

= 0.913 x 300 290 mm \ D =d+2xcover =

281.50 mm 290 +

2

x 30

= 320 mm

8 mm dia links and a nominal cover of = 12 mm Fbar will be used. With 25 mm 320 25 8 D = 12 / 2 = 281 Hence ok. The total depth is much less than assumed value. However recalculation is not necessary, because self weight of lintel is compratively smaller than the super imposed load. Assuming that

4 Steel Reiforcement :3 x 10 = 371.56 mm2 x 281 2 x dia = 3.14 x 12 x 12 using x 100 4 x 100 / 113 = 3.29 say = 4 mm Fbar, Hence Provided 4 bars of 12 2 having, Ast = 4 x 113 = 452.16 mm 0.85 Min reinforcement is given by = Ast/A = fy 0.85 x( 300 x 290 )= 2 Taking fy = 415 178 Nmm , Ast= 415 Since actual reinforcement provided is > than the design reinforcement . Hence O.K. Bend 2 Bar at a distance = L / 7 = 2.30 / 7 = 0.30

BM

21704 sst x j x D 230 x 0.904 3.14 12 mmfbars Area = 4 Nomber of Bars = Ast/A = 372

Ast =

=

From the face of of each s. Keep a nominal cover =

25

= 113

mm2

No.

mm2 m 300 mm

mm

5 Check for shear and design of shear reinforcement :The reaction at wall will be uniformly distributed over the full width Hence the shear force will be maximum at edge of . (As the edge wl 32822 x 2 Maximum V = = = 32822 N of aupport) 2 2 32822 tv = V/bd = = 0.389 N / mm2 300 x 281 1 At b suppoprt, x 452.16 = 226.1 mm2 2 At b suppoprt, 100Ast 100 x 226 = = 0.268 % 300 x 281 bd Hence from Table permissible shear (tc)for M 20 concrete, for 0.268 % steel = 0.210 N/mm2 Hence shear reinforcement is required. tc .bd = 0.210 x Vc = 300 x 281 = 17703 N V = #### - 17703 = 15119 N \ Vs V = c Shear rasistance V s1 of bent up bars is Vs1

ssv

= =

-

0.707 x

Asv sin a = 230

0.707ssv x ASv

x 226.1 =

36763 N

But Vs1 Assined to inclined bars can not be more than = = Using

1/2

8

ssv x Asv x d Vs1

[email protected]

7559.5 N only

mm 2-ldg. Strirrups Ast

Sv =

x 15119 =

1/2Vs

= =

2 230

3.14 x 4 x 100.5 x 7559.5 x

8 x 8 = 100.5 x 100 281 = 859 mm

mm2

However, maximum spacing corresponding to nominal shear strirrups is given by Sv < 2.18 x 100.5 x 415 2.175 xAsv xFy = = 302 mm b 300.00 0.75 x 281 = 211 mm Subject to lesser than of (0.75xd or 300mm) = Hence provide the 8 mm strirrups @ 210 mm c/c throughout. 2 x 8 mmF holding bars at top Provide 6 Check for devlopment length at s :The code stipulates that at the simple s, where reinforcement is confined 1.3xM1 by a compressive reaction, the diameter of the reinforcement be such that + L0 > Ld V 1 Ast = x 452.16 = 226.1 mm2 2 M1 = moment of resistance of section, assuming all reinforcementstress sst M1

V

"= Ast xs st x jc d = 226.1 x 230

x

0.904

x

= 32822

\

Ld

=

N

Alternatively, Ld = 45F Taking bars straight Ls we have, Ld =( x' 2 1.3 xM1 L0 + = 1.3 V = 648 7 Details of reinforcement:-

[email protected]

281

= 13.21 x

Fsst or 4tbd

12

4

x

10 6 N-mm x 1.6

230 x 0.8

= 45 x 12 = 540 mm in the , without any hook or bend with x' 300 = - 25.00 = 125 mm 2 13.21 x 10 6 x + 125 = 648 mm 32822 > 539.1 Hence Code requirement are satisfied

= 539.1 mm

=

25

mm

0.30 0.4 0.66 10

cm Lime concrete

60 0

60 0 Slab

16 cm RCC slab

2.16

1.50 1.80

60 0

60 0 Lintel Beam 2.00 2.60

1.4

0.8

Floor

0.30

Design of Lintel Beam (when height is less) 8

mm F 2 - lgd strirrups @

210 mm c/c 2 8

mm F anchor bars

210

300

4 -

210

12 mm F bars

300

2000 300 mm

2 -

8 mm F anchor bars

8

mm F bars 25 mm 2 -

8 mm F 2 Lgd strirrups @ 210 mm c/c

300 mm

250 250 mm

25 mm 4 - 12 mm F bars Section at mid span

2 - 12 mm F bars section at

12 mm F bars

VALUES OF DESIGN CONSTANTS Grade of concrete Modular Ratio

M-15 18.67

M-20 13.33

M-25 10.98

M-30 9.33

M-35 8.11

M-40 7.18

scbc N/mm2 m scbc

5

7

8.5

10

11.5

13

93.33

93.33

93.33

93.33

93.33

93.33

kc

0.4

0.4

0.4

0.4

0.4

0.4

(a) sst = 140 N/mm2 (Fe 250)

jc

0.867

0.867

0.867

0.867

0.867

0.867

Rc

0.867

1.214

1.474

1.734

1.994

2.254

Pc (%)

0.714

1

1.214

1.429

1.643

1.857

kc

0.329

0.329

0.329

0.329

0.329

0.329

jc

0.89

0.89

0.89

0.89

0.89

Rc

0.89 0.732

1.025

1.244

1.464

1.684

1.903

Pc (%)

0.433

0.606

0.736

0.866

0.997

1.127

kc

0.289

0.289

0.289

0.289

0.289

0.289

jc

0.904

0.904

0.904

0.904

0.904

0.904

Rc

0.653

0.914

1.11

1.306

1.502

1.698

Pc (%)

0.314

0.44

0.534

0.628

0.722

0.816

kc

0.253

0.253

0.253

0.253

0.253

0.253

jc

0.916

0.916

0.916

0.914

0.916

0.916

Rc

0.579

0.811

0.985

1.159

1.332

1.506

Pc (%)

0.23

0.322

0.391

0.46

0.53

0.599

(b) sst = 190 N/mm2 (c ) sst = 230 N/mm2 (Fe 415) (d) sst = 275 N/mm2 (Fe 500)

Permissible shear stress Table tv in concrete (IS : 456-2000) 100As bd < 0.15 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 and above

Permissible shear stress in concrete M-15 M-20 M-25 M-30 0.18 0.18 0.19 0.2 0.22 0.22 0.23 0.23 0.29 0.30 0.31 0.31 0.34 0.35 0.36 0.37 0.37 0.39 0.40 0.41 0.40 0.42 0.44 0.45 0.42 0.45 0.46 0.48 0.44 0.47 0.49 0.50 0.44 0.49 0.51 0.53 0.44 0.51 0.53 0.55 0.44 0.51 0.55 0.57 0.44 0.51 0.56 0.58 0.44 0.51 0.57 0.6

tv N/mm2 M-35 M-40 0.2 0.2 0.23 0.23 0.31 0.32 0.37 0.38 0.42 0.42 0.45 0.46 0.49 0.49 0.52 0.52 0.54 0.55 0.56 0.57 0.58 0.60 0.60 0.62 0.62 0.63

Maximum shear stress tc.max in concrete (IS : 456-2000) Grade of concrete

tc.max

M-15 1.6

M-20 1.8

M-25 1.9

M-30 2.2

M-35 2.3

M-40 2.5

Grade of concrete tbd (N / mm2)

Shear stress tc 100As M-20 bd 0.15 0.18 0.16 0.18 0.17 0.18 0.18 0.19 0.19 0.19 0.2 0.19 0.21 0.2 0.22 0.2 0.23 0.2 0.24 0.21 0.25 0.21 0.26 0.21 0.27 0.22 0.28 0.22 0.29 0.22 0.3 0.23 0.31 0.23 0.32 0.24 0.33 0.24 0.34 0.24 0.35 0.25 0.36 0.25 0.37 0.25 0.38 0.26 0.39 0.26 0.4 0.26 0.41 0.27 0.42 0.27 0.43 0.27 0.44 0.28 0.45 0.28 0.46 0.28 0.47 0.29 0.48 0.29 0.49 0.29 0.5 0.30 0.51 0.30 0.52 0.30 0.53 0.30 0.54 0.30 0.55 0.31 0.56 0.31 0.57 0.31 0.58 0.31 0.59 0.31 0.6 0.32 0.61 0.32 0.62 0.32

Reiforcement % 100As M-20 bd 0.18 0.15 0.19 0.18 0.2 0.21 0.21 0.24 0.22 0.27 0.23 0.3 0.24 0.32 0.25 0.35 0.26 0.38 0.27 0.41 0.28 0.44 0.29 0.47 0.30 0.5 0.31 0.55 0.32 0.6 0.33 0.65 0.34 0.7 0.35 0.75 0.36 0.82 0.37 0.88 0.38 0.94 0.39 1.00 0.4 1.08 0.41 1.16 0.42 1.25 0.43 1.33 0.44 1.41 0.45 1.50 0.46 1.63 0.46 1.64 0.47 1.75 0.48 1.88 0.49 2.00 0.50 2.13 0.51 2.25

0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14

0.32 0.32 0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.36 0.36 0.36 0.36 0.36 0.36 0.37 0.37 0.37 0.37 0.37 0.37 0.38 0.38 0.38 0.38 0.38 0.38 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.4 0.4 0.4 0.4 0.4 0.4 0.4

1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66

0.4 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.46 0.46 0.46 0.46

1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18

0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.50 0.50 0.50 0.50 0.50 0.50

2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70

0.50 0.50 0.50 0.50 0.50 0.50 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15

0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.51

Permissible Bond stress Table tbd in concrete (IS : 456-2000) Grade of concreteM-10 -tbd (N / mm2)

M-15 0.6

M-20 0.8

M-25 0.9

M-30 1

M-35 1.1

M-40 1.2

M-45 1.3

Development Length in tension Plain M.S. Bars

H.Y.S.D. Bars

Grade of concrete

tbd (N / mm2)

kd = Ld F

tbd (N / mm2)

kd = Ld F

M 15

0.6

58

0.96

60

M 20

0.8

44

1.28

45

M 25

0.9

39

1.44

40

M 30

1

35

1.6

36

M 35

1.1

32

1.76

33

M 40

1.2

29

1.92

30

M 45

1.3

27

2.08

28

M 50

1.4

25

2.24

26

Permissible stress in concrete (IS : 456-2000) Grade of concrete M M M M M M M M M

10 15 20 25 30 35 40 45 50

Permission stress in compression (N/mm 2) Permissible stress in bond (Average) for Bending acbc Direct (acc) plain bars in tention (N/mm2) (N/mm2) 3.0 5.0 7.0 8.5 10.0 11.5 13.0 14.5 16.0

Kg/m2 300 500 700 850 1000 1150 1300 1450 1600

(N/mm2) 2.5 4.0 5.0 6.0 8.0 9.0 10.0 11.0 12.0

Kg/m2 250 400 500 600 800 900 1000 1100 1200

(N/mm2) -0.6 0.8 0.9 1.0 1.1 1.2 1.3 1.4

in kg/m2 -60 80 90 100 110 120 130 140

00) M-50 1.4