**Design of shear wall:**

The vertical structural element of a reinforced concrete framed structure which is provided to resist in-plane lateral loads is known as shear wall. The design of shear wall is necessary to resist the in-plane shear and in-plane flexural moment caused by lateral loads through the vertical cantilever Action. Here we discuss about the design of shear wall located around the lift.

**Design a shear wall of a building which is located in three side if the lift as shown. Grade of concrete = M25 and grade of steel = Fe 500**

Total length of the wall = 192 + 90*3+15*4+9*2= 549 in. = 13.9446 m.

Floor height = 3.2004 m.

Wall thickness = 9 in. = 0.2286 m.

The stepwise design of shear wall procedure is as follows:

**Check for slenderness ratio:**

Eff. Height of wall, he = 0.75H = 0.75*3.2004 = 2.4003m

Slenderness ratio, he/t = 2.4003/0.2286 = 10.50 < 30 OK.

Min. eccentricity, E min = e = 0.05t **(Clause 32.2.2, IS 456:2000)**

= 0.05*0.2286=0.01143m = 11.43mm

Additional eccentricity (ea) = he2/2500t

= 2.40032/ (2500*0.2286) = 0.010813m = 10.813 mm

**Calculation of load:**

- Ground floor:

Length = 13.9446 m

Height =2.798/2+3.2004/2 = 2.9992m.

Load = 25*13.9446*2.9992*0.2286 = **239.01 **KN

2. Typical Floor:

Length = 13.9446 m

Height = 3.2004/2+3.2004/2 = 3.2004 m

Load = 25*13.9446*3.2004*0.2286 = **255.05 **KN

3. Second last Floor:

Length = 13.9446 m.

Height = 3.2004/2+2.8956/2 = 3.048m.

Load = 25 * 13.9446 * 3.048 * 0.2286 = **242.90 **KN

4. Top Floor:

Length = 13.9446 m

Height = 2.8956/2 = 1.4478

Load = 25*13.9446*1.4478*0.2286 = 115.3808 KN

Roof load:

Plan area = 192β * 90β = 4.8768 m * 2.286 m = 11.1483 m2.

Slab thickness = 150 mm = 0.15 m

Slab load = 11.1483*0.15*25 = 41.80 KN.

Total Top Floor Load = 115.3808 + 41.80 =**157.18 KN**

Total load = 239.01+9*255.05+242.90+157.18 = **2934.54 KN**

**Calculation of base shear:**

Total seismic weight of lift (**W**) = **2934.54 KN**

Height, h = **37.698m**

Base shear, V_{b} = A_{h}*W **(Clause 7.5.3, IS 1893 (Part 1) : 2002)**

Where,

A_{h} = design horizontal acceleration spectrum

W = seismic weight as per **(Clause 7.4.2, IS 1893 (Part 1) : 2002)**

Now, A_{h} = ππΌπ_{a}/2π
π **(Clause 6.4.2, IS 1893 (Part 1) : 2002)**

Where,

Z = zone factor = 0.36 for Seismic Zone V **(Table 2, IS 1893 (Part 1) : 2002)**

I = importance factor = 1 **(Table 6, IS 1893 (Part 1) : 2002)**

R = response reduction factor=5 **(Table 7, IS 1893 (Part 1) : 2002)**

S_{a}/g = average response acceleration coefficient

**Width of Shear wall:**

D_{Y} = 4.8768 m.

D_{X} = 2.2860 m

Time Period (TA) = 0.09ββπ **(Clause 7.6.2, IS 1893 (Part 1) : 2002)**

TAy = 0.09β37.698β4.8768

=1.53 sec.

TAx = 0.09β37.698β2.2860

= 2.24 sec.

**For soil type of type II**

For TAy =1.53 sec.

(Sa/g)Y = 1.361.53 = 0.88

Ahy=0.36*1*0.88 / (2*5)

=0.031

Again, For TAx = 2.24 sec.

(Sa/g)X = 1.362.24 =0.607

Ahx =0.36*1*0.607 / (2*5)

=0.022

Now,

Base shear (Vby) = Ahy*W = 0.033*2934.54 = 90.97 KN

Base shear (Vbx) = Ahx*W = 0.022*2934.54 = 64.56 KN

The deign axial strength of a wall per unit length,

Puw = 0.3(t-1.2e-2ea) f_{ck} **(Clause 32.2.5, IS 456 : 2000)**

Where, t= thickness of the wall

e = eccentricity

ea = additional eccentricity due to slenderness effect taken as Hwe^{2}/2500t.

Puw = 0.3(228.60-1.2*11.43-2*10.813)*25 = 1460.41 N/mm.

**Calculation for main vertical reinforcement:**

Assume clear cover 15 mm. and 12mm dia. bars.

**When lateral load is acting along X – direction:**

Mu/3 = 1.5β1840.876/3 = 920.438 KNm

Vu/3= 1.5β64.56/3 = 32.28 KN

Pu/3= 1.5β2934.54 /3 = 1467.27 KN

dβ/D = (15+6)/4876.80 = 0.0043. (Adopt 0.05)

Mu/fckbd^{2} = 920.438*106/ (25*228.60*2286^{2}) = 0.0308

Pu/fckbd = 1467.27*1000/ (25*2286*228.60) = 0.1123

Using chart 35 SP 16:

p/fck = 0.00

Check for minimum reinforcement:

Ast, min = 0.0025 * bD = 0.0025*228.60*2286 = 1306.45 mm2.

Ab = π * 12^{2}/4 = 113.0973 mm2

Spacing of bars = 2286 * 113.0973 / 1306.45 = 197.89 mm.

Check for spacing of bar

Spacing β€ 3t or 450 mm whichever is less

=3*228.6 or 450mm

=685.8 or 450 **OK**

To take account of opposite phenomena, Provide 12 mm dia bar @ 180mm c/c on both sides.

**When lateral force is acting along Y-direction**

Mu= 1.5 * 2761.59 = 3891.576 KNm

Vu=1.5 * 96.381 = 136.455 KN

Pu= 1.5 * 2934.54 = 4401.81 KN

dβ/D = (15+6)2286 = 0.0091. Adopt 0.05.

Mu/fckbd^{2} = 3891.576*106/ (25*228.60*4876.80^{2}) = 0.029

Pu/fckbd = 4401.81*1000/ (25*4876.80*228.60) = 0.157

Using chart 35 SP 16:

p/fck = 0

Ast, min = 0.0025*228.60*4876.80=2787.09mm2

Ab = Ο*12^{2}/4 = 113.0973 mm2

Spacing of bars = 4876.80*113.0973/2787.09= 197.89mm

Check for spacing of bar

Spacing β€ 3t or 450 mm whichever is less.

= 3*228.6 or 450 mm

= 685.8 or 450 OK

To take account of opposite phenomena, Provide 12 mm dia bar @ 180mm c/c on both sides.

**Calculation of Horizontal steel reinforcement:**

Area of horizontal steel reinforcement = 0.25% bH = 0.0025*228.60*3200.4 = 1829.0286 mm2.

Provide 12mm dia. bars.

Ab = Ο *12^{2}/4 = 113.0973 mm2.

Spacing of bars = 3200.4*113.0973/1829.0286 = 197.90 mm.

Provide 12mm dia. bars @180mm c/c on both face.

**Check for shear:**

**Along Y- direction (long wall):**

**As per Clause 32.4.2, IS 456 : 2000**

Nominal shear stress, π_{v} = V_{u}/td

Where, V_{u} = Shear force due to design loads.

t = wall thickness.

d = 0.8 * Lw where Lw is the length of the wall.

Here, πv = Vu/ (t*0.8*Lw) = 144.57*103/ (228.60*0.8*4876.80) =0.162 N/mm2

Allowable shear stress, πa = 0.17fck = 0.17*25 = 4.25 N/mm2 > πv.

Design shear strength of concrete:

Hw/Lw = 3200.4/4876.80 = 0.6563 < 1.

π_{cw} = (3.0-Hw/Lw) Kl βf_{ck} = (3.0-0.6563)*0.2*β25 = 2.34 N/mm2 > πv.

Hence safe.

**Along X- direction (short wall):**

**As per Clause 32.4.2, IS 456 : 2000**

Nominal shear stress, π_{v} = Vu/td

Where, Vu = Shear force due to design loads.

t = wall thickness.

d = 0.8 * Lw where Lw is the length of the wall.

Here, πv = Vu/td = Vu/ (t*0.8*Lw) = 96.84*103/ (228.60*0.8*2286)

= 0.2316 N/mm2

Allowable shear stress, πa = 0.17fck = 0.17*25 = 4.25 N/mm2 > πv.

Design shear strength of concrete

Hw/Lw = 3200.4/2286 = 1.4 > 1.

πcw = (π»π€/πΏπ€+1)/(π»π€*πΏπ€β1) * K_{2}βfck = (1.4+1)/(1.4β1) *0.045*β25 = 1.35 N/mm2 > πv.

**Hence safe.**

**Summary:**

**Vertical reinforcement:**

**Provide 12 mm dia bar @ 180 mm c/c on both sides along X-direction.**

**Provide 12 mm dia bar @ 180 mm c/c on both sides along Y-direction.**

**Horizontal reinforcement:**

Provide 12mm dia. bars @180 mm c/c on both face.

**Anchorage Length:**

Ld + 10b_{d }= 0.87βππ¦βπ·/4 π_{ππ} + 10*12 = 0.87β500β12/4β1.4β1.6 + 10*12 = 702.59mm.