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Materials & Civil

Structural, construction, and materials-engineering formulae.

Stress

Basic
σ=FA\sigma = \frac{F}{A}

Internal force per unit cross-sectional area.

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Strain

Basic
ε=ΔLL0\varepsilon = \frac{\Delta L}{L_0}

Fractional deformation under load.

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Young Modulus

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

Ratio of stress to strain; measures material stiffness.

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Factor of Safety

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

Ratio of a material strength to the actual applied stress.

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Cantilever Beam Deflection

Advanced
δ=FL33EI\delta = \frac{F L^3}{3 E I}

Maximum deflection of a cantilever with an end load.

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Rectangular Area Moment of Inertia

Advanced
I=bh312I = \frac{b h^3}{12}

Second moment of area for a rectangular cross-section.

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Bending Stress

Advanced
σ=McI\sigma = \frac{M c}{I}

Stress in a beam due to a bending moment.

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Concrete Mix Volume

Basic
V=Vc+Vs+VgV = V_c + V_s + V_g

Total volume from cement, sand, and gravel parts.

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Uniformly Distributed Load

Basic
w=WLw = \frac{W}{L}

Load per unit length of a beam.

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Max Moment (Simple Beam, UDL)

Advanced
Mmax=wL28M_{max} = \frac{w L^2}{8}

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

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Linear Thermal Expansion

Intermediate
ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T

Change in length due to temperature change.

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Density

Basic
ρ=mV\rho = \frac{m}{V}

Mass per unit volume of a material.

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Slenderness Ratio

Advanced
λ=Ler\lambda = \frac{L_e}{r}

Ratio governing column buckling.

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Euler Buckling Load

Advanced
Pcr=π2EI(KL)2P_{cr} = \frac{\pi^2 E I}{(K L)^2}

Critical axial load at which a column buckles.

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Hydraulic Radius

Intermediate
Rh=APR_h = \frac{A}{P}

Cross-sectional flow area divided by wetted perimeter.

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Water-Cement Ratio

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

Ratio controlling concrete strength and workability.

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