Dead load of structure (constant)

Concrete slab = Slab Thickness x Density of concrete= 0.15m x 0.24 kN/m3

= 3.6 kN/m2

Brick Wall = Wall Height x Thickness x Density of brick= 3.5m x 0.15m x 19 kN/m3

= 9.975 kN/m2

Dead-load factor = 1.4

Live load of rooms (constant)

Living Room = 1.5 kN/m2

Dining Room= 1.5 kN/m2

Dry Kitchen = 1.5 kN/m2

Wet Kitchen = 1.5 kN/m2

Terrace = 1.5 kN/m2

WC = 1.5 kN/m2

Store = 1.5 kN/m2

Guest Room = 1.5 kN/m2

Bedroom = 1.5 kN/m2

Balcony = 1.5 kN/m2

Live-load factor = 1.6

Analysis of Beams

Ly = Longer side of slabLx = Shorter side of slab

Ly / Lx = 2 or > 2 , One way slab Ly / Lx < 2 , Two way slab

Ground Floor Level Plan

`Slab 6-4, D-A = 4000/3525

= 1.134 (< 2)= Two way slab

Slab 4-2, D-A = 4000/1500= 2.667 (> 2)= One way slab

Slab 4-1, E-D = 4255/2050= 2.075 (> 2)= One way slab

First Floor Level Plan

Slab 7, G-F = 3000/2287= 1.311

= Two way slab

Slab 6, G-F = 3000/2287= 1.311= Two way slab

Slab 7-6, F-E = 4575/3000= 1.525= Two way slab

Slab 6-5, G-F = 3000/1500= 2= One way slab

Slab 5-4, G-F = 3000/2025= 1.481= Two way slab

Slab 6-4, F-C = 6950/3525= 1.971= Two way slab

Slab 4-2, F-D = 6000/1500= 4= One way slab

Ground Floor Beam A, 6-4

Dead load:Slab 6-4, D-ABrickwallBeam Self-weight

Live load:Slab 6-4, D-A

Total Dead load

Dead load on slab 6-4, D-A= Dead load on slab x Lx/2`= 3.6 kN/m2 x (3.525m)/2= 6.345 kN/m

Dead load on brick wall A6-A4= 9.975 kN/m

Beam Self weight= Beam size x concrete density= 0.23m x 0.5m x 24kN/m3

= 2.76 kN/m

Total Dead load= 6.345 + 9.975 + 2.76= 19.08 kN/m

Total Live loadLive load on slab 6-4, D-A= Live load on slab x Lx/2= 1.5 kN/m2 x (3.525m)/2= 5.287 kN/m

Total Ultimate loadTotal Ultimate dead load = Total dead load x 1.4= 19.08 kN/m x 1.4= 26.71 kN/m

Total Ultimate live load= Total live load x 1.4= 5.287 kN/m x 1.4= 7.4 kN/m

Total Ultimate load= 26.71 + 7.4= 34.11 kN/m

ΣFy = 0RA6y = RA4y

= (34.11 x 3.525) / 2= 60.12 kN

Sheer Force DiagramAt point A6 there is a 60.12 kN force acting upwards (+ve)

At the middle of the beam, there is no point load, thus UDL was converted to PL only for calculation of reaction forces. 34.11 kN/m x 1.7625m = 60.12 kN60.12 kN – 60.12 kN = 0

At point B there is a 60.12 kN force acting downwards (-ve)0 kN – 60.12 kN = - 60.12kN

Bending Moment DiagramAt point A6, there is only a line so no area = 0 kNmAt middle point, A1 = A2

= ½ x 1.7625 x 60.12kN = 52.98 kNm

At point A4, Area of triangle (+ve) + area of triangle (-ve)

= 52.98 – 52.98= 0 kNmGround Floor Beam D-B, 4

Dead load:Slab 6-4, D-ASlab 4-2, D-ABrickwallBeam Self-weight

Live load:Slab 6-4, D-ASlab 4-2, D-A

Total Dead loadDead load on slab 6-4, D-B= Dead load on slab x Lx/2= 3.6 kN/m2 x (2.630m)/2= 9.468 kN/m

Dead load on slab 4-2, D-B= Dead load on slab x Lx/2= 3.6 kN/m2 x (2.630m)/2= 9.468 kN/m

Dead load on brick wall D4-B4= 9.975 kN/m

Beam Self weight= Beam size x concrete density= 0.15m x 0.5m x 24kN/m3

= 1.8 kN/m

Total Dead load= 9.468 + 9.468 + 9.975 + 1.8= 30.71 kN/m

Total Live loadLive load on slab 6-4, D-A= Live load on slab x Lx/2= 1.5 kN/m2 x (2.63m)/2= 1.9725 kN/m

Live load on slab 4-2, D-A= Live load on slab x Lx/2= 1.5 kN/m2 x (2.63m)/2= 1.9725 kN/m

Total live load= 1.9725 + 1.9725= 3.945 kN/m

Total Ultimate loadTotal Ultimate dead load = Total dead load x 1.4= 30.71 kN/m x 1.4= 42.994 kN/m

Total Ultimate live load= Total live load x 1.4= 3.945 kN/m x 1.4= 5.523 kN/m

Total Ultimate load= 42.994 + 5.523= 48.517 kN/m

ΣFy = 0RAy = RBy

= (48.517 kN/m x 2.63m) / 2= 63.79 kN

Sheer Force DiagramAt point D there is a 63.79 kN force acting upwards (+ve)At the middle of the beam, there is no point load, thus UDL was converted to PL only for calculation of reaction forces. 48.517 kN/m x 1.315 m = 63.79 kN63.79 kN – 63.79 kN = 0

At point B there is a 63.79 kN force acting downwards (-ve)0 kN – 63.79 kN = - 63.79 kN

Bending Moment DiagramAt point D, there is only a line so no area = 0 kNAt middle point, A1 = A2

= ½ x 1.315 x 63.79 N = 41.941 kNm

At point B, Area of triangle (+ve) + area of triangle (-ve)

= 41.941 – 41.941= 0 kNmGround Floor Beam D, 4-1

Dead load:Slab 4-1, E-DBrick wall D, 4-2Beam Self-weightBeam D-A, 2

Live load:Slab 4-1, E-DSlab 4-2, D-A

Calculation for Beam D-A, 2Dead load:Slab 4-2, D-ABeam self-weight

Live load:Slab 4-2, D-A

Total Dead loadDead load on slab 4-2, D-A= Dead load on slab x Lx/2= 3.6 kN/m2 x (1.5m)/2= 2.7 kN/m

Beam Self weight= Beam size x concrete density= 0.15m x 0.5m x 24kN/m3

= 1.8 kN/m

Total Dead load= 2.7 + 1.8= 4.5 kN/m

Total Live loadLive load on slab 4-2, D-A= Live load on slab x Lx/2= 1.5 kN/m2 x (1.5m)/2= 1.125 kN/m

Total Ultimate loadTotal Ultimate dead load = Total dead load x 1.4= 4.5 kN/m x 1.4= 6.3 kN/m

Total Ultimate live load= Total live load x 1.4= 1.125 kN/m x 1.6= 1.8 kN/m

Total Ultimate load= 6.3 + 1.8= 8.1 kN/m

ΣFy = 0RDy = RAy

= (8.1 kN/m x 4.0m) / 2= 16.2 kN

Beam D, 4-1Total Dead loadDead load on slab 4-1, E-D= Dead load on slab x Lx/2= 3.6 kN/m2 x (2.050m)/2= 3.69 kN/m

Brickwall D, 4-2= 9.975 kN/m

Beam Self weight= Beam size x concrete density= 0.15m x 0.5m x 24kN/m3

= 1.8 kN/m

Total Dead load from D4 to D2= 3.69 + 9.975 + 1.8= 15.465 kN/m

Total Dead load from D2 to D1= 3.69 + 1.8= 5.49 kN/m

Total Live loadLive load on slab 4-1, E-D= Live load on slab x Lx/2= 1.5 kN/m2 x (2.050m)/2= 3.075 kN/m

Total Ultimate loadTotal Ultimate dead load D4-D2= Total dead load x 1.4= 15.465 kN/m x 1.4= 21.651 kN/m

Total Ultimate dead load D2-D1= Total dead load x 1.4= 5.49 kN/m x 1.4= 7.686 kN/m

Total Ultimate live load D4-D2= Total live load x 1.6= 4.2 kN/m x 1.6= 6.72 kN/m

Total Ultimate live load D4-D1= Total live load x 1.6= 3.075 kN/m x 1.6= 4.92 kN/m

Total Ultimate load D4-D2= 21.651 + 6.72= 28.371 kN/m

Total Ultimate load D2-D1= 7.686 + 4.92= 12.606 kN/m

ΣMD4 = 00 = -4.255(RD1y) + [28.371 x 1.5 x (1.5/2)] + (16.2 x 1.5) + [12.606 x 2.755 x (2.755/2)] RD1y = 104.057/4.255RD1y = 24.455 kN

ΣFy = 00 = RD4 y + RD1 y – 16.2 – (1.5 x 28.371) – (12.606 x 2.755)RD4 y = 69.031 kN

Sheer Force DiagramAt point D4 there is a 69.031 kN force acting upwards (+ve)UDL was converted to PL only for calculation of reaction forces. 28.371 kN/m x 1.5 m = 42.5565 kN69.031 kN – 42.5565 kN = 26.4745 kN

At point D2 there is a 16.2 kN force acting downwards (-ve)26.4745 kN – 16.2 kN = 10.2745 kN

At point D1 there is a 12.606 kN force acting downwards (-ve)12.606 kN/m x 2.755m = 34.729 kN

10.2745 kN – 34.729 kN = -24.455 kNBending Moment DiagramAt point D4, there is only a line so no area = 0 kN

At point D2, ½ x (69.031 + 26.475) x 1.5m = 71.63 kNm

At point D2 to mid point,½ x (10.275) x 2.755m = 14.15 kNm

At point D1, force is acting downwards. (-ve)-½ x 24.455 x 2.1275 = -26.014 kNm

First Floor Beam F-D, 4

Dead load:Slab 4-2, F-DSlab 6-4, F-CBrickwallBeam Self-weight

Live load:Slab 4-2, F-DSlab 6-4, F-C

Total Dead loadDead load on slab 4-2, F-D= Dead load on slab x Lx/2= 3.6 kN/m2 x (1.500)/2= 2.7 kN/m

Dead load on slab 6-4, F-C= Dead load on slab x Lx/2= 3.6 kN/m2 x (3.525)/2= 6.345 kN/m

Dead load on brick wall D4-B4= 9.975 kN/m

Beam Self weight= Beam size x concrete density= 0.15m x 0.6m x 24kN/m3

= 2.16 kN/m

Total Dead load= 2.7 + 6.345 + 9.975 + 2.16= 21.18 kN/m

Live load on slab 4-2, F-D= Live load on slab x Lx/2= 1.5 kN/m2 x (1.5m)/2= 1.125 kN/m

Live load on slab 6-4, F-C= Live load on slab x Lx/2= 1.5 kN/m2 x (3.525m)/2= 5.2875 kN/m

Total live load = 1.125 + 5.2875= 6.4125 kN/m

Total Ultimate loadTotal Ultimate dead load = Total dead load x 1.4= 21.18 kN/m x 1.4= 29.652 kN/m

Total Ultimate live load= Total live load x 1.6= 1.125 kN/m x 1.6= 1.575 kN/m

Total Ultimate load= 6.3 + 1.575= 7.875 kN/m

ΣFy = 0RFy = RDy

= (7.875 kN/m x 6.0m) / 2= 23.625 kN

Sheer Force DiagramAt point D there is a 23.625 kN force acting upwards (+ve)At the middle of the beam, there is no point load, thus UDL was converted to PL only for calculation of reaction forces. 7.875 kN/m x 3 m = 23.625 kN23.625 kN – 23.625 kN = 0

At point B there is a 23.625 kN force acting downwards (-ve)0 kN – 23.625 kN = - 23.625 kN

Bending Moment DiagramAt point D, there is only a line so no area = 0 kNAt middle point, A1 = A2

= ½ x 3.0 x 23.625 N = 35.4375 kNm

At point B,

Area of triangle (+ve) + area of triangle (-ve)= 23.625 – 23.625= 0 kNmFirst Floor Beam F, 6-4

Dead load:Slab G-F, 5-4Slab F-C, 6-4Beam Self-weight

Calculation for secondary beam, Beam G-F, 5Dead load:Slab G-F, 6-5Slab G-F, 5-4Beam Self-weight

Total dead loadDead load on slab G-F, 6-5= Dead load on slab x Lx/2= 3.6 kN/m2 x (1.5)/2= 2.7 kN/m

Dead load on slab G-F, 5-4= Dead load on slab x Lx/2= 3.6 kN/m2 x (2.025)/2= 3.645 kN/m

Beam Self-weight= Beam size x concrete density= 0.15m x 0.7m x 24kN/m3

= 2.52 kN/m

Total Dead load= 2.7 + 3.645 + 2.52= 8.865 kN/mTotal Ultimate loadTotal Ultimate dead load= Total dead load x 1.4= 8.865 kN/m x 1.4= 12.411 kN/m

ΣFy = 0RGy = RFy

= (12.411 kN/m x 3.0m) / 2= 18.6165 kN

Beam F, 6-4Total Dead loadDead load on slab 5-4, G-F= Dead load on slab x Lx/2 x 2/3= 3.6 kN/m2 x (2.025)/2 x 2/3= 4.86 kN/m

Dead load on slab 6-4, F-C= Dead load on slab x Lx/2 x 2/3= 3.6 kN/m2 x (3.525)/2 x 2/3= 4.23 kN/m

Beam Self weight= Beam size x concrete density= 0.15m x 0.6m x 24kN/m3

= 2.16 kN/m

Total Dead load F6-F5= 4.23 + 2.16= 6.39 kN/m

Total Dead load F5-F4= 4.86 + 4.23 + 2.16= 11.25 kN/m

Total Ultimate loadTotal Ultimate dead load F6-F5= Total dead load x 1.4= 6.39 kN/m x 1.4= 8.946 kN/m

Total Ultimate dead load F5-F4

= Total dead load x 1.4= 11.25 kN/m x 1.4= 15.75 kN/m

Load diagramΣMF6 = 00 = -3.525(RF4y) + (18.6165 x 1.5) + [15.75 x 2.025 x (2.025/2)] + [8.946 x 1.5 x (1.5/2)]RF4y = 70.281/3.525RF4y = 19.938 kN

ΣFy = 00 = RF6 y + RF4 y – 18.6165 – (8.946 x 1.5) – (15.75 x 2.025)RF6 y = 43.99 kN

Sheer Force DiagramAt point F6 there is a 43.99 kN force acting upwards (+ve)UDL was converted to PL only for calculation of reaction forces. 8.946 kN/m x 1.5 m = 13.419 kN43.99 kN – 13.419 kN = 30.571 kN

At point F5 there is a 18.6165 kN force acting downwards (-ve)30.571 kN – 18.6165 kN = 11.9545 kN

At point F4 there is a (15.75 x 2.025) kN force acting downwards (-ve)15.75 x 2.025= 31.894 kN

11.9545 – 31.894 kN = -19.9395 kN

Bending Moment DiagramAt point F6, there is only a line so no area = 0 kN

At point F5, ½ x (43.99 + 30.571) x 1.5m = 55.92 kNm

At point F5 to midpoint,½ x (11.9545) x 0.2625m = 1.569 kNm

At point F4, force is acting downwards. (-ve)-½ x 19.938 x 1.7625 = -26.014 kNm

First Floor Beam F, 7-6

Dead load:Slab G-F, 7-6Slab F-E, 7-6Beam Self-weight

Calculation for secondary Beam G-F, 6.5Dead load:Slab G-F, 7-6Beam self-weight

Total dead loadDead load on slab G-F, 7-6= Dead load on slab x Lx/2= 2 [3.6 kN/m2 x (2.2875)/2]= 8.235 kN/m

Beam Self-weight= Beam size x concrete density= 0.15m x 0.7m x 24kN/m3

= 2.52 kN/m

Total Dead load= 8.235 + 2.52= 10.755 kN/m

Total Ultimate loadTotal Ultimate dead load= Total dead load x 1.4= 10.755 kN/m x 1.4= 15.057 kN/m

ΣFy = 0RGy = RFy

= (15.057 kN/m x 3.0m) / 2= 22.585 kN

Beam F, 7-6Total Dead loadDead load on slab 7-6.5, G-F= Dead load on slab x Lx/2 x 2/3= 3.6 kN/m2 x (2.2875)/2 x 2/3= 2.745 kN/m

Dead load on slab 6.5-6, G-F= Dead load on slab x Lx/2 x 2/3= 3.6 kN/m2 x (2.2875)/2 x 2/3= 2.745 kN/m

Dead load on slab 7-6, F-E= Dead load on slab x Lx/2= 3.6 kN/m2 x (3.000)/2= 5.4 kN/m

Beam Self weight= Beam size x concrete density= 0.15m x 0.6m x 24kN/m3

= 2.16 kN/m

Total Dead load F7-F6.5= 2.745 + 5.4= 8.145 kN/m

Total Dead load F6.5-F5= 2.745 + 5.4= 8.145 kN/m

Total Ultimate load

Total Ultimate dead load F7-F6.5/F6.5-F6= Total dead load x 1.4= 8.145 kN/m x 1.4= 11.403 kN/m

Load diagramΣMF7 = 00 = -3.525(RF6y) + (22.59 x 1.762) + 2[11.403 x 1.762 x (1.762/2)] RF6y = 75.206/3.525RF6y = 21.335 kN

ΣFy = 00 = RF7 y + RF6 y – 22.59 – 2(11.403 x 1.762)RF7 y = 41.439 kN

Sheer Force DiagramAt point F7 there is a 41.439 kN force acting upwards (+ve)UDL was converted to PL only for calculation of reaction forces. 11.403 kN/m x 1.762 m = 20.092 kN41.439 kN – 20.092 kN = 21.347 kN

At point F6.5 there is a 22.59 kN force acting downwards (-ve) 21.347 kN – 22.59 kN = -1.243 kN

At point F6 there is a (11.403 x 1.762) kN force acting downwards (-ve)11.403 x 1.762 = 20.092 kN

-1.243 – 20.092 kN = -21.335 kN

Bending Moment DiagramAt point F6, there is only a line so no area = 0 kN

At point F7, ½ x (41.439) x 1.762m = 36.507 kNm

At point F6, force is acting downwards. (-ve)-½ x (1.243+21.335)x 1.7625 = -19.897kNm

Columns

Column G7Area of load acting on the column G7= 1.5m x (4.575/2)m= 2.2875 x 1.5= 3.431 m2

Ground floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (1.5+2.2875)

= 8.181 kN

Slab = 3.6 kN/m2 x 3.431 m2

= 12.351 kN

Live loadTerrace = 1.5 kN/m2 x 3.431 m2

= 5.1465 kN

First floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (1.5+2.2875)

= 8.181 kN

Slab = 3.6 kN/m2 x 3.431 m2

= 12.351 kN

Wall = 9.975 kN/m x (1.5+2.2875)= 37.78 kN

Live loadBalcony = 1.5 kN/m2 x 3.431 m2

= 5.1465 kN

Total load acting on column = 8.181+12.351+5.1465+8.181+12.351+37.78+5.1465

= 89.137 kN

Column F6Area of load acting on the column F6= [1.5m x 2.2875m] + [3.475 x 2.2875m] + [1.975 x 1.7625] + [1.7625 x 1.5]= 17.505 m2

Ground floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (1.5+1.14375+3.0+0.75)

= 13.8105 kN

Slab = 3.6 kN/m2 x 17.505 m2

= 63.018 kN

Wall = 9.975 kN/m x (1.7625+2.2875)= 40.398 kN

Live loadTerrace = 1.5 kN/m2 x (2.2875 x 1.5)

= 5.15 kNTerrace = 1. 5 kN/m2 x (1.7625 x 1.5)

= 3.965 kNDry kitchen = 1. 5 kN/m2 x (2.2875 x 3.475)

= 11.923 kNDining = 1. 5 kN/m2 x (1.975 x 1.7625)

= 5.221 kN

First floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (1.5+1.14375+3.0+0.75)

= 13.8105 kN

Slab = 3.6 kN/m2 x 17.505 m2

= 63.018 kN

Wall = 9.975 kN/m x (1.7625+2.2875+1.5+1.975)= 75.061 kN

Live loadBalcony = 1.5 kN/m2 x (2.2875 x 1.5)

= 5.15 kN Balcony = 1.5 kN/m2 x (1.7625 x 1.5)

= 3.965 kNBedroom = 1.5 kN/m2 x (2.2875 x 1.975)

= 6.776 kNMaster room = 1.5 kN/m2 x (1.7625 x 1.975)

= 5.221 kN

Total load acting on column = 13.8105 + 63.018 + 40.398 + 5.15 + 3.965 + 11.923 + 5.221 + 13.8105 + 63.018 +75.061 + 5.15 + 3.965 + 6.776 + 5.221= 316.487 kN

Column F2Area of load acting on the column F2= [0.75m x 1.975m] + [0.75m x 1.975m]= 2.9625 m2

Ground floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (0.75+1.3775)

= 4.5954 kN

Slab = 3.6 kN/m2 x 2.9625 m2

= 10.665 kN

Wall = 9.975 kN/m x (0.75+1.3775)= 21.222 kN

First floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (0.75+3.0)

= 8.1 kN

Slab = 3.6 kN/m2 x 2.9625 m2

= 10.665 kN

Wall = 9.975 kN/m x (0.75+3.0)= 37.406 kN

Live loadBalcony = 1.5 kN/m2 x (0.75x3.0)

= 3.375 kN

Total load acting on column = 4.5954 + 10.665 + 21.222 + 8.1 + 10.665 + 37.406 + 3.375= 96.0284 kN

Column B4Area of load acting on the column B4= [1.37 x 1.7625] + [0.75m x 2.475m]= 4.2708 m2

Ground floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (0.685+0.685)

= 2.9592 kN

Slab = 3.6 kN/m2 x 4.2708 m2

= 15.375 kN

Wall = 9.975 kN/m x (0.685+0.685)= 13.665 kN

Live loadGuestroom = 1.5 kN/m2 x (1.37x1.7625)

= 3.622 kN

First floorDead loadBeam = (0.15 x 0.6 x 24kN/m3) x (0.685+0.685+1.0125)

= 5.1462 kN

Slab = 3.6 kN/m2 x 4.2708 m2

= 15.375 kN

Wall = 9.975 kN/m x (0.685+0.685+1.0125)= 23.765 kN

Live loadMaster bedroom= 1.5 kN/m2 x (1.315x1.7625)

= 3.476 kNMaster bath = 1.5 kN/m2 x (0.685x1.0125)

= 1.040 kN

Total load acting on column = 2.9595 + 15.375 + 13.665 + 3.622 + 5.1462 + 15.375 + 23.765 + 3.476 + 1.040= 84.4237 kN