Civil Engineering

Solve ax² + bx + c = 0.

Determinant of a 2×2 matrix.

Force from mass and acceleration.

Horizontal range of a projectile launched from ground.

Period of a small-angle simple pendulum.

pH from hydrogen-ion concentration.

Moment about a point.

Kinetic or static friction on a horizontal surface.

Axial stress under a direct load.

Engineering strain from elongation.

Modulus of elasticity from stress and strain.

Stress from restrained thermal expansion.

Ratio of ultimate to working stress.

Max central deflection of a simply supported beam under a mid-span point load.

Fiber stress from bending moment.

Critical buckling load for a slender column.

Pressure at depth in a fluid column.

Flow regime indicator for pipe flow.

Solve for outlet velocity given inlet area, velocity and outlet area.

Free-jet velocity from a reservoir under head h.

Frictional head loss in a pipe.

Shaft power required to lift fluid at flow rate Q against head H.

Cement, sand and aggregate for a nominal 1 : n : m mix (M20 ≈ 1:1.5:3). Dry volume = 1.54 × wet volume.

Water demand from cement quantity and w/c ratio.

Void ratio and porosity from soil volumes.

Gravimetric water content of soil.

Terzaghi effective stress from total stress and pore pressure.

Seepage discharge through soil.

SSD on a level road (IRC).

Required superelevation on a horizontal curve.

Number of standard bricks (190×90×90 mm nominal, 200×100×100 mm with mortar) per m³ of masonry.

Unit weight of a steel bar using the d²/162 rule.

Cement and sand for plastering; dry volume factor 1.33.

Total water demand from population and per-capita usage.

Mass of chlorine required per day.

Beta-distribution expected activity time.