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Beam Analysis
- 1. Beam Analysis Calculation GroundFloor Beam, G-F/ 7 Beam Self Weight = Beam Size x Concrete Density = 0.15m x 0.3m x 24 kN/m3 = 1.08 kN/m2 Wall Self Weight = Wall Height x Wall Thickness x Brick density = 3m x 0.15m x 19 kN/m2 = 8.55 kN/m2 Dead Load on slab A (Two way slab) Load is transferred to beam G7-F7 in a UDL form Dead load from slab A = Dead load on slab x (Lx /2) x 2/3 = 3.6 kN/m2 x (2.66m /2) x 2/3 = 3.192 kN/m2 Total Dead Load= 1.08 kN/m2 + 8.55 kN/m2 + 3.192 kN/m2 = 12.822 kN/m2 Live Load on Slab A (Two way slab) Load is transferred to beam G7-F7 in a UDL form Live load from slab A = Live load factor x (Lx /2) x 2/3 = 1.5 kN/m2 x (2.66m /2) x 2/3 = 1.33 kN/m2 Ultimate Load Diagram Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load = 12.82 kN/m2 x 1.4 = 17.95 kN/m Live Load = 1.33 kN/m2 x 1.6 = 2.13 kN/m Ultimate load = 17.95 kN/m2 + 2.13 kN/m2 = 20.08 kN/m2
- 2. Reaction Force ∑M =0 = RF7 (2.66) – 20.08(2.66)(2.66/2) = 2.66 RF7 – 71.04 kN/m2 RF7 = 26.706 kN/m2 ∑Fy = 0 = RF7 + RG7 – 20.08(2.66) RG7 = 26.706 kN/m2 Shear Force Diagram Area (+) = 1/2 x 26.706 x (2.66/2) = 17.759 Area (-) = 1/2 x 26.706 x (2.66/2) = 17.759 Bending Moment Diagram
- 3. Beam Analysis Calculation GroundFloor Beam, F/ 5-8 Beam Self Weight = Beam Size x Concrete Density = 0.15m x 0.3m x 24 kN/m3 = 1.08 kN/m2 Wall Self Weight = Wall Height x Wall Thickness x Brick density = 3m x 0.15m x 19 kN/m2 = 8.55 kN/m2 Dead Load on slab A (Two way slab) Load is transferred to beam F5-7 in a UDL form Dead load from slab A = Dead load on slab x (Lx /2) = 3.6 kN/m2 x (2.66m /2) = 4.79 kN/m2 Dead Load on slab B (Two way slab) Load is transferred to beam F5-8 in a UDL form Dead load from slab B = Dead load on slab x (Lx /2) x 2/3 = 3.6 kN/m2 x (4.7m /2) x 2/3 = 5.64 kN/m2 Total Dead Load F5-7 = 1.08 kN/m2 + 8.55 kN/m2 + 4.79 kN/m2 + 5.64 kN/m2 = 20.06 kN/m2 Total Dead Load F5-8 = 1.08 kN/m2 + 8.55 kN/m2 + 5.64 kN/m2 = 15.27 kN/m2
- 4. Live Load onSlab A (Two way slab) Load is transferred to beam F5-7 in a UDL form Live load from slab A = Live load factor x (Lx /2) = 1.5 kN/m2 x (2.66m /2) = 2 kN/m2 Live Load on Slab B (Two way slab) Load is transferred to beam F5-8 in a UDL form Live load from slab B = Live load factor x (Lx /2) x 2/3 = 1.5 kN/m2 x (4.7 /2) x 2/3 = 2.35 kN/m2 Total Live load F5-7 = 2 kN/m2 + 2.35 kN/m2 = 4.35 kN/m2 Total Live load F5-8 = 2.35 kN/m2 Ultimate Load Diagram Apply factor 1.4 and 1.6 to dead load and live load F5-7 respectively. Dead load = 20.06 kN/m2 x 1.4 = 28.084 kN/m Live Load = 4.35 kN/m2 x 1.6 = 6.96 kN/m Ultimate load = 28.084 kN/m + 6.96 kN/m = 35.044 kN/m Apply factor 1.4 and 1.6 to dead load and live load F5-8 respectively. Dead load = 15.27 kN/m2 x 1.4 = 21.378 kN/m Live Load = 2.35 kN/m2 x 1.6 = 3.76 kN/m Ultimate load = 21.378 kN/m2 + 3.76 kN/m2 = 25.138 kN/m2 Reaction Force ∑M = 0 = RF5 (4.7) – 2.7(140.176) – 0.7(26.706) – 0.35(17.597) = 4.7 RF5 – 403.328 kN/m2 RF5 = 85.815 kN/m2 ∑Fy = 0 = RF5 + RF8 – 140.176 – 26.706 – 17.597 RF8 = 184.479 kN/m2 – 85.815 kN/m2 = 98.664 kN/m2
- 5. Shear Force Diagram x/54.36= 4/140.176 x= 1.55 Area (+) = 1/2 x 85.815 x (4 – 1.55) = 105.123 Area (-) = 1/2 x 54.361 x 1.55 + 1/2 x 0.7 x (81.067 + 98.664 ) = 105.036 Bending Moment Diagram
- 6. Beam Analysis Calculation FirstFloor Beam, XY Beam Self Weight = Beam Size x Concrete Density = 0.15m x 0.3m x 24 kN/m3 = 1.08 kN/m2 Wall Self Weight = Wall Height x Wall Thickness x Brick density = 3m x 0.15m x 19 kN/m2 = 8.55 kN/m2 Dead Load on slab A (Two way slab) Load is transferred to beam xy in a UDL form Dead load from slab A = Dead load on slab x (Lx /2) = 3.6 kN/m2 x (1.85m /2) = 3.33 kN/m2 Dead Load on slab B (Two way slab) Load is transferred to beam xy in a UDL form Dead load from slab B = Dead load on slab x (Lx /2) = 3.6 kN/m2 x (2.05m /2) = 3.69 kN/m2 Total Dead Load= 1.08 kN/m2 + 8.55 kN/m2 + 3.33 kN/m2 + 3.69 kN/m2 = 16.65 kN/m2
- 7. Live Load onslab A (Two way slab) Load is transferred to beam xy in a UDL form Live load from slab A = Live load factor x (Lx /2) = 1.5 kN/m2 x (1.85m /2) = 1.388 kN/m2 Live Load on slab B (Two way slab) Load is transferred to beam xy in a UDL form Live load from slab B = Live load factor x (Lx /2) = 1.5 kN/m2 x (2.05m /2) = 1.538 kN/m2 Total Live Load= 1.388 kN/m2 + 1.538 kN/m2 = 2.926 kN/m2 Ultimate Load Diagram Apply factor 1.4 and 1.6 to dead load and live load respectively. Dead load = 16.65 kN/m2 x 1.4 = 23.31 kN/m Live Load = 2.926 kN/m2 x 1.6 = 4.682 kN/m Ultimate load = 23.31 kN/m2 + 4.682 kN/m2 = 27.992 kN/m2 Reaction Force ∑M = 0 = RX (2.435) – 27.992(2.435)(2.435/2) = 2.435 RX – 82.985 kN/m2 RX = 34.08 kN/m2 ∑Fy = 0 = RX + RY – 27.992(2.435) RY = 68.16 kN/m2 – 34.08 kN/m2 = 34.08 kN/m2
- 8. Shear Force Diagram Area(+) = 1/2 x 34.08 x (2.435/2) = 20.746 Area (-) = 1/2 x 34.08 x (2.435/2) = 20.746 Bending Moment Diagram
- 9. Beam Analysis Calculation FirstFloor Beam, E-C/ 2 Beam Self Weight = Beam Size x Concrete Density = 0.15m x 0.3m x 24 kN/m3 = 1.08 kN/m2 Wall Self Weight = Wall Height x Wall Thickness x Brick density = 3m x 0.15m x 19 kN/m2 = 8.55 kN/m2 Dead Load on slab A (Two way slab) Load is transferred to beam E2-X in a UDL form Dead load from slab A = Dead load on slab x (Lx /2) x 2/3 = 3.6 kN/m2 x (1.85m /2) x 2/3 = 2.22 kN/m2 Dead Load on slab B (Two way slab) Load is transferred to beam X-C2 in a UDL form Dead load from slab B = Dead load on slab x (Lx /2) x 2/3 = 3.6 kN/m2 x (2.05m /2) x 2/3 = 2.46 kN/m2 Total Dead Load E2-X = 1.08 kN/m2 + 8.55 kN/m2 + 2.22 kN/m2 = 11.85 kN/m2 Total Dead Load X-C2 = 1.08 kN/m2 + 8.55 kN/m2 + 2.46 kN/m2 = 12.09 kN/m2
- 10. Live Load onslab A (Two way slab) Load is transferred to beam E2-X in a UDL form Live load from slab A = Live load factor x (Lx /2) x 2/3 = 1.5 kN/m2 x (1.85m /2) x 2/3 = 0.925 kN/m2 Live Load on slab B (Two way slab) Load is transferred to beam X-C2 in a UDL form Live load from slab B = Live load factor x (Lx /2) x 2/3 = 1.5 kN/m2 x (2.05 /2) x 2/3 = 1.025 kN/m2 Ultimate Load Diagram Apply factor 1.4 and 1.6 to dead load and live load E2-X respectively. Dead load = 11.85 kN/m2 x 1.4 = 16.59 kN/m Live Load = 0.925 kN/m2 x 1.6 = 1.48 kN/m Ultimate load = 16.59 kN/m + 1.48 kN/m = 18.07 kN/m Apply factor 1.4 and 1.6 to dead load and live load X-C2 respectively. Dead load = 12.09 kN/m2 x 1.4 = 16.026 kN/m Live Load = 1.025 kN/m2 x 1.6 = 1.64 kN/m Ultimate load = 16.926 kN/m2 + 1.64 kN/m2 = 18.566 kN/m2 Reaction Force ∑M = 0 = RE2 (3.9) – 33.43(2.975) – 34.08(2.05) – 38.06(1.025) = 3.9 RE2 – 208.3298 kN/m2 RE2 = 53.418 kN/m2 ∑Fy = 0 = RE2 + RC2 – 33.43 – 34.08 – 36.06 RC2 = 105.57 kN/m2 – 53.418 kN/m2 = 52.152 kN/m2
- 11. Shear Force Diagram Area(+) = 1/2 x 1.85(53.418 + 19.988) = 67.9 Area (-) = 1/2 x 2.05(52.152 + 14.092) = 67.9 Bending Moment Diagram