Materials & Civil

Structural, construction, and materials-engineering formulae.

Materials & Civil brings together the core formulas used to understand how structures and materials behave under real-world loads, temperature changes, and design limits. Whether you’re a student revising for exams or a professional working on buildings, beams, concrete, or construction calculations, these equations help you size components safely, predict deflection and stress, and make sound engineering decisions.

Stress

\sigma = \frac{F}{A}

Internal force per unit cross-sectional area.

Strain

\varepsilon = \frac{\Delta L}{L_0}

Fractional deformation under load.

Young Modulus

E = \frac{\sigma}{\varepsilon}

Ratio of stress to strain; measures material stiffness.

Factor of Safety

FoS = \frac{\sigma_{ult}}{\sigma_{allow}}

Ratio of a material strength to the actual applied stress.

Cantilever Beam Deflection

\delta = \frac{F L^3}{3 E I}

Maximum deflection of a cantilever with an end load.

Rectangular Area Moment of Inertia

I = \frac{b h^3}{12}

Second moment of area for a rectangular cross-section.

Bending Stress

\sigma = \frac{M c}{I}

Stress in a beam due to a bending moment.

Concrete Mix Volume

V = V_c + V_s + V_g

Total volume from cement, sand, and gravel parts.

Uniformly Distributed Load

w = \frac{W}{L}

Load per unit length of a beam.

Max Moment (Simple Beam, UDL)

M_{max} = \frac{w L^2}{8}

Maximum bending moment for a simply supported beam under uniform load.

Linear Thermal Expansion

\Delta L = \alpha L_0 \Delta T

Change in length due to temperature change.

Density

\rho = \frac{m}{V}

Mass per unit volume of a material.

Slenderness Ratio

\lambda = \frac{L_e}{r}

Ratio governing column buckling.

Euler Buckling Load

P_{cr} = \frac{\pi^2 E I}{(K L)^2}

Critical axial load at which a column buckles.

Hydraulic Radius

R_h = \frac{A}{P}

Cross-sectional flow area divided by wetted perimeter.

Water-Cement Ratio

w/c = \frac{m_{water}}{m_{cement}}

Ratio controlling concrete strength and workability.