These structural calculators cover mechanics of materials applied to structural members: normal stress from axial load, engineering strain, Hooke's law (E = σ/ε), bending moment in simply supported beams with distributed or concentrated loads, allowable stress verification, and moment of inertia for rectangular cross-sections using Navier's formula. All calculations operate within the linear-elastic domain (small deformations, isotropic homogeneous material).
Note: Advisory domain: results are useful for preliminary sizing and order-of-magnitude verification. Any structural calculation intended for construction requires verification by a licensed professional engineer per applicable building codes.
σ = N / A [Pa = N/m²]. N is the axial force [N], A is the cross-sectional area [m²]. σ > 0 = tension; σ < 0 = compression. In structural design, typically expressed in [MPa] = [N/mm²].
Engineering strain ε
ε = ΔL / L₀ [dimensionless]. ΔL is elongation or shortening, L₀ is initial length. In the linear-elastic range: ε = σ / E (Hooke's law). Typical values for steel under load: ε ≈ 10⁻³–10⁻².
For simply supported beam: M_max = q×L²/8 (distributed load q [N/m], span L [m]), or M_max = F×L/4 (point load F at midspan). Bending moment is in [N·m] and causes flexural stresses in the cross-section.
Navier's formula
σ = M × y / I_x [Pa]. M is the bending moment [N·m], y is the distance from the neutral axis [m], I_x is the second moment of area about the neutral axis [m⁴]. For rectangular section b×h: I_x = b×h³/12; W_x = I_x/(h/2) = b×h²/6 [m³].
Allowable stress
σ_allowable = f_y / γ_M [MPa]. f_y is the yield strength (A36 steel: f_y = 250 MPa / 36 ksi; A572 Gr.50: 345 MPa / 50 ksi), γ_M is the partial safety factor for material (per Eurocode or AISC LRFD).