Bolted and Threaded Joint Design Suite

Screen bolt preload, tightening torque, dynamic load sharing, thread strength, engagement, and joint stiffness for metric, UNC, and UNF fasteners.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Joint inputs

Choose the mode matching the design question. Fractions and friction coefficients are positive magnitudes; dynamic force entries are load ranges.

Metric thread dmmStandard coarse metric size M1–M42.Property class Rₘ.RₚISONominal steel strength class.Preload fraction αRₚ₀.₂Initial tensile stress divided by yield strength; 0 < α ≤ 1.Thread friction μₜ—60° flank friction coefficient.Under-head friction μ_b—Bearing-face friction coefficient.

Screening result

Primary result

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How to use

Select the mode for torque/preload, dynamic loading, engagement/stripping, stiffness, or UNC/UNF screening.
Choose the thread and grade, then enter every required value in the displayed units. Use positive load magnitudes; C is the bolt load-share fraction.
Select Calculate. The canonical result and secondary values update together; Reset restores the metric preload example.
Interpret warnings as a failed screening condition, not a safe design. Verify thread series, grade, lubrication, friction, and load convention independently.
Do not use this model for prevailing-torque fasteners, eccentric/prying loads, gaskets, plastic joints, nonstandard thread geometry, fatigue spectra, or code compliance without a detailed joint analysis.

Equations used

Metric geometry: d₀=(d₂+d₃)/2; Aₜ=πd₀²/4; Rₚ₀.₂=kRₘ. Preload mode: σₜ=αRₚ₀.₂; Fᵢ=σₜAₜ. Torque: ρ=atan[μₜ/cos(30°)]; φ=atan[P/(πd₂)]; M_G=Fᵢ(d₂/2)tan(φ+ρ); M_WD=Fᵢμ_b(1.3d/2); M_A=M_G+M_WD; τ=M_G/(πd₃³/16); σ_e=√(σₜ²+3τ²).

Target-stress mode solves Fᵢ=qRₚ₀.₂ / √[(1/Aₜ)²+3{(d₂/2)tan(φ+ρ)/(πd₃³/16)}²]. Dynamic endurance uses σ_a=0.75(180/d+52), F₀.₂=Rₚ₀.₂Aₜ, ΔF_b=2σ_aAₜ, ΔFₘ=ΔF_b(1−C)/C, Fᵢ,min=Fₘ+ΔFₘ, and Fᵢ,max=F₀.₂−ΔF_b.

Dynamic load envelope starts with Fₘ=qₘF₀.₂ and the endurance equations above. If Fᵢ,max−(ΔF_b+ΔFₘ)<Fₘ or Fᵢ,min>Fᵢ,max, it applies the limiting branch F_B=F₀.₂−Fₘ; ΔF_b=CF_B; ΔFₘ=(1−C)F_B; then recomputes Fᵢ,min=Fₘ+ΔFₘ and Fᵢ,max=F₀.₂−ΔF_b. qₘ is the required residual clamp ratio; Fₘ is residual clamp force; C is the bolt load-share fraction; ΔF_b and ΔFₘ are the bolt/member load-range portions; Fᵢ,min and Fᵢ,max are preload limits; F_B is the total dynamic external-load range. Forces are calculated in N and displayed in kN. The limiting branch identifies a capacity boundary, not proof of fatigue safety.

Engagement: τ₂=r₂σ₂; A_req=RₘAₜ/τ₂; Lₑ=0.8r₁Rₘd/(r₂σ₂). Stripping: A_th=0.5(3.1426)d₀Lₑ; F_strip=τᵤA_th. Stiffness: k_b=πd²E_b/(4l_m); d₂c=1.5d; d₃c=d₂c+l_m tan30°; A_m=π{[(d₂c+d₃c)/2]²−d²}/4; k_m=A_mE_m/l_m; C=k_b/(k_b+k_m).

Unified 60° threads: P=1/N; d_p=d−0.649519/N; d_r=d−1.299038/N; Aₜ=π[(d_p+d_r)/2]²/4; Fᵢ=αS_pAₜ. UNC/UNF torque and stress use the same ρ, φ, M_G, M_WD, τ, and σ_e relations in inch–lbf–kpsi units.

Theory and method

The suite combines standard 60° thread geometry with a friction-angle torque model, von Mises tension–torsion screening, an elementary two-spring joint load partition, and simplified thread-shear areas. α and q are fractions, not percentages. Torque sign is positive for tightening; a negative backdrive component indicates self-locking tendency under the chosen friction—not guaranteed resistance to loosening.

Assumptions include concentric axial loading, elastic members, uniform friction, a 30° half-angle thread flank, bearing friction acting at 0.65d radius, and uniform engaged-thread shear. Grade tables are nominal screening properties. Check current ISO 898-1, ASME B1.1, SAE J429, and a detailed method such as VDI 2230 for production design.