Design a preloaded bolted joint that carries tension without separating or yielding — proof-based preload, the joint stiffness split that decides how little external load actually reaches the bolt, tightening torque, and safety factors against yield, separation and slip.
Sp = proof strength (MPa), Sy = yield.
Bolt is steel, E 207 GPa. Softer members shift more load onto the bolt.
Leave 0 to compute C from stiffnesses. Typical well-designed metal joints: 0.15–0.30.
Shared across all n bolts.
Bolt tension starts at the preload and rises only along the shallow slope C as external load grows — a stiff joint keeps the bolt nearly constant. Where the clamp-force line hits zero, the joint separates and the bolt suddenly carries everything.
Preload. Fi = f · Sp · At, with f = 0.75 for reusable, 0.90 for permanent joints. Tightening torque T = K · Fi · d, where the nut factor K bundles all the thread and head friction — the single biggest source of preload scatter (±25% is common).
Joint stiffness split. The bolt and clamped members act as two springs. The joint constant C = k_bolt / (k_bolt + k_member) is the fraction of external load the bolt feels. Bolt stiffness k_b = A_b·E_b/grip; member stiffness uses the Shigley frustum (cone) model. Because members are usually far stiffer than the bolt, C is small (0.15–0.30) and the bolt barely notices the external load — that's the entire point of preloading.
Bolt load & separation. Max bolt tension Fb = Fi + C·P_bolt. Clamp force remaining = Fi − (1−C)·P_bolt; it reaches zero — the joint separates — at P_sep = Fi/(1−C). Below separation the bolt sees only C·P of the fluctuating load, which is why preloaded joints have excellent fatigue life.
Slip (shear). A friction-type joint resists shear through clamp force: capacity = μ · n · Fi, checked against the applied shear. If it slips, the bolts go into direct shear/bearing, which this tool flags but doesn't size.
Static analysis. Fatigue-critical joints need the alternating bolt stress (C·P_alt/2At) checked against the endurance limit with a Goodman line — not performed here.