Mechanical Engineering Calculators: Bolted Joint Clamped-Member Stiffness Calculator

Symmetric compression-zone model

This V1 calculator represents the clamped material around one concentric through-hole. Equal effective bearing faces at the top and bottom generate identical axisymmetric compression frusta that spread toward the joint midplane.

For a frustum of thickness t, minor outer diameter D_b, through-hole diameter D_h, elastic modulus E, and half-angle θ, the implemented NASA-derived stiffness is:

With no active diameter limit, each frustum has thickness L/2. Because both elements carry the same compressive load, their flexibility terms add:

Diameter-limited compression zone

If D_lim < D_natural, the compression zone reaches the user-established limit before the midplane. The end-frustum thickness and remaining central-cylinder thickness are:

The middle region uses the constant annular area A_lim = π(D_lim² − D_h²)/4. Its flexibility is added in series:

When D_lim = D_b, the limiting case is a constant annular cylinder across the full thickness. A limit-triggered engineering warning reminds the user to verify the actual boundary evidence.

Worked example

Use the default inputs:

1. The unrestricted midplane diameter is 18 + 20 tan(30°) = 29.547005 mm.
2. Because 40 mm > 29.547005 mm, the diameter limit is inactive and each frustum is 10 mm thick.
3. Each frustum stiffness is 2184.848857 kN/mm.
4. Two identical frusta in series give k_c = K_f/2 = 1092.424428 kN/mm.
5. The equivalent uniform annular area is 312.121265 mm², corresponding to an equivalent outer diameter of 22.768512 mm around the 11 mm hole.

This example validates the stated model only. It does not select the compression angle, effective bearing diameter, diameter limit, member material, or joint acceptance criteria.

Input evidence and interpretation

D_b is a modeling diameter, not automatically the physical washer outside diameter. Verify the load-transfer face required by the selected method. D_lim is also not derived here: free edges, neighboring compression zones, plate shape, washers, counterbores, inserts, and local geometry can require a different representation.

The equivalent annular area and outer diameter are mathematical summaries that reproduce calculated stiffness over the entered total thickness and modulus. They are not actual contact dimensions. The compliance-share bar shows how much modeled displacement comes from the two frusta versus the central constant-area region.

Use the Bolt Axial Stiffness Calculator for a compatible k_b, then transfer both stiffnesses to the Bolted Joint Load Sharing and Separation Calculator. Load introduction and stiffness still must represent compatible physical regions.

For a stack with three distinct layer moduli or unequal bearing faces, continue with the Multi-Layer Bolted Joint Clamped-Member Stiffness Calculator. The expanded model still requires external evidence for interfaces, compression angles, and geometric limits.

Engineering scope and limitations

The calculator excludes:

• automatic selection of compression half-angle, effective bearing diameter, washer behavior, or maximum compression-zone diameter;
• multiple materials, stacked-member interfaces, different moduli, unequal upper and lower geometry, blind holes, inserts, tapped joints, counterbores, and countersinks;
• finite plate width, asymmetric free edges, interacting neighboring compression zones, noncircular boundaries, and automatic bolt-spacing or edge-distance derivation;
• Poisson effects, washer and coating compliance, local indentation, plate bending, contact nonlinearity, partial contact, plasticity, creep, temperature gradients, and preload redistribution;
• bolt stiffness, load-introduction factor, preload, external load distribution, prying, separation, leakage, slip, loosening, strength, fatigue, fracture, and thread checks;
• safety-factor selection, governing-standard interpretation, qualification, manufacturing feasibility, or engineering approval.

Use an element-by-element stiffness model, finite-element analysis, or test when geometry, layering, interfaces, contact, or load introduction falls outside this symmetric homogeneous approximation.