Seismic Base Shear

Find the approximate period Ta from Cl 7.6.2, read Sa/g for that period and soil type, then work out Ah = (Z/2)(I/R)(Sa/g) and multiply by the seismic weight: Vb = Ah × W. For example, Zone III, I = 1.0, R = 5, medium soil, a 15 m RC frame and W = 20,000 kN give Ah = 0.0381 and Vb = 761 kN.

For a bare RC moment frame Ta = 0.075h^0.75, for a bare steel moment frame Ta = 0.085h^0.75, and for RC frames with masonry infill Ta = 0.09h/√d, with h and d in metres. A 15 m building with a 16 m base dimension gives Ta = 0.09 × 15 / 4 = 0.338 s by the infill formula, against 0.572 s as a bare RC frame.

Cl 7.2.2 and Table 7 set a floor on the base shear of ρW, with ρ = 0.7 % in Zone II, 1.1 % in Zone III, 1.6 % in Zone IV and 2.4 % in Zone V. It usually governs tall, flexible buildings in low zones: a 60 m RC frame on rock in Zone II has Ah = 0.0062 from the spectrum, so the 0.007 minimum controls and Vb = 700 kN for W = 100,000 kN.

For the equivalent static method, Cl 6.4.2(a) keeps Sa/g flat at 2.5 from T = 0 up to the corner period of the soil type. The 1 + 15T ramp below 0.1 s applies only to the response spectrum method, so this calculator does not use it.

It does not check torsion or scale results from a response spectrum analysis (Cl 7.7.3), and it covers only the moment-frame R values of 3 and 5. The storey table needs the dead load of each floor from you, including half the walls and columns of the storeys above and below it (Cl 7.4.1); it does not take off quantities from a model.

Each floor counts its full dead load plus a share of its imposed load: 25 % when the imposed load is 3.0 kN/m² or less and 50 % when it is more (Cl 7.3.1, Table 10). Imposed load on the roof is not counted (Cl 7.3.2). For a G+4 frame of 300 m² floors with 10 kN/m² dead and 3.0 kN/m² imposed, each floor is (10 + 0.25 × 3.0) × 300 = 3,225 kN, the roof at 8 kN/m² is 2,400 kN, and W = 4 × 3,225 + 2,400 = 15,300 kN.

Cl 7.6.3 gives Qi = Vb × Wi·hi² / Σ Wj·hj², with hi measured from the base. For the G+4 building above with 3.2 m storeys, Zone III, medium soil, I = 1.2 and R = 5, Vb = 665.9 kN and the roof takes 665.9 × 60,000 / 156,750 = 254.9 kN, the fourth floor 219.2 kN and the first floor only 13.7 kN. The storey shear below each level is the sum of the forces at and above it, so the ground storey carries the full 665.9 kN.