Timber Embedment Strength for Dowel-Type Fasteners
Computes the characteristic embedment strength of timber parallel to the grain, for dowel-type fasteners, from f_h,0,k = 0.082·(1 − 0.01·d)·ρ_k, with the fastener diameter d in millimetres and the characteristic timber density ρ_k in kg/m³, returning MPa. Embedment is the local crushing of the wood under the fastener shank, and it — not the bolt strength — usually governs the capacity of a connection with dowels, pins or through bolts, because timber yields long before steel does. The expression, adopted by Eurocode 5 and by the Brazilian NBR 7190:2022, shows that larger fasteners mobilise a LOWER average stress: going from 8 to 20 mm diameter cuts embedment strength by 13 %, which in practice favours many slender fasteners over a few thick ones, provided minimum spacings are respected. It is valid for fasteners up to about 30 mm. Enter the fastener diameter and the characteristic timber density.
Result
—
Timber Embedment Strength for Bolts and Dowel Fasteners
Anyone designing a timber connection with dowels, pins or through bolts runs into the same quantity: embedment strength, the local crushing of wood under the fastener shank. It feeds the Johansen equations that give connection capacity, and it decides whether a truss node needs four 12 mm dowels or two 20 mm ones. This page solves the characteristic expression for load parallel to the grain from two inputs the designer already has at hand: the fastener diameter and the characteristic timber density.
The expression reads f_h,0,k = 0.082 · (1 − 0.01·d) · ρ_k, with d in millimetres, ρ_k in kg/m³ and the result in MPa. The (1 − 0.01·d) term encodes a test finding: a thicker fastener mobilises a lower average stress, since bearing pressure under the shank grows less uniform. With the page defaults — a 12 mm fastener and ρ_k = 350 kg/m³ — the output is 25.26 MPa; the same timber with an 8 mm fastener gives 26.40 MPa and with 20 mm gives 22.96 MPa, the 13 % drop quoted above. An independent check: at d = 1 mm this expression gives 28.41 MPa while the separate equation for nails driven without pre-drilling, 0.082·ρ_k·d^(−0.3), gives 28.70 MPa — two distinct fits within 1 %.
The value holds parallel to the grain only. Load at an angle calls for the k_90 factor and a Hankinson-type combination this page leaves out, and reusing the parallel value at any angle sits on the unsafe side. The formula covers dowels and bolts in pre-drilled holes up to roughly 30 mm, and the field rejects anything larger. A nail driven without pre-drilling follows another equation: at 3.4 mm it yields 19.88 MPa against 27.72 MPa here, a 28 % gap. And ρ_k means characteristic density, the 5 % quantile, never the average of your batch. Finally, the output is a characteristic strength: k_mod, the partial factor and the failure mode still stand between it and connection capacity.
Frequently asked questions
Should I enter mean density or characteristic density?
Does it apply to nails driven without pre-drilling?
Is the result already the capacity of the connection?
Related Tools
Timber Design Strength (kmod, NBR 7190)
Computes the timber design strength per the Brazilian NBR 7190, f_d = k_mod1 · k_mod2 · k_mod3 · f_k / γ_w, where the three modification factors correct the characteristic strength for load duration, service moisture class and timber grade, and γ_w is the material partial safety factor. Timber is the only common structural material whose strength falls with the DURATION of the applied load, and that is what k_mod1 encodes: it is 1.10 for instantaneous action and only 0.60 for permanent load, so the same member is worth nearly twice as much under impact as under self weight. In the most common design combination — long-duration action (0.70), moisture class 1 or 2 (1.00), first-grade sawn timber (1.00) and compression parallel to the grain with γ_wc = 1.4 — the factors cancel such that the design strength comes out exactly half the characteristic value, a shortcut worth memorising to sanity-check any result. Enter the three modification factors, the characteristic strength and the partial safety factor.
Bolt Count for Shear
Calculate the number of bolts needed to resist a shear force, n = F ÷ (A·τ_adm), from the total shear force to transmit F (N), each bolt's area A (mm²) and the material's allowable shear stress τ_adm (MPa). In structural and mechanical connections loaded in shear (beam splices, truss connections, flanges under lateral load, splice plates), the force is distributed among several bolts, each working in shear. The number needed is the total force divided by one bolt's shear capacity (area × allowable stress). The result is rounded up, and in practice a quantity is adopted that also meets minimum bolt spacing, edge distance and connection symmetry criteria. This calculation is the basis of designing bolted connections in steel structures (where it competes with welding) and in machines: it sets how many bolts and of what diameter are needed. There are other checks in the same connection: plate BEARING (contact pressure on the hole wall, which can tear the plate before the bolt shears), edge tear-out and the plate's own net-section strength (minus the holes). But bolt shear is the starting point. Enter the shear force, each bolt's area and the allowable stress.
Box Compression Strength (McKee)
Estimates the vertical compression strength of a corrugated box with the simplified McKee formula, BCT = 5.87 × ECT × √(board caliper × box perimeter), where ECT — the edge crush resistance measured per TAPPI T 811 (ISO 3037) — is in newtons per millimetre and both dimensions are in millimetres. The result, in newtons, is the load an empty box withstands in the laboratory compression test, with the board conditioned at 23 °C and 50% relative humidity. Because strength grows with the square root of the perimeter and linearly with ECT, doubling the perimeter buys only 41% more, while switching to a flute with 30% higher ECT buys the full 30% — upgrading the board usually beats reshaping the box. For real pallet stacking, divide the BCT by a safety factor of 3 to 5, which covers the stiffness lost to ambient humidity, the creep of board under load over weeks and the misalignment between boxes in the column. Enter the ECT, the board caliper and the box perimeter.
Junction Temperature
Calculate the junction temperature of a power semiconductor, T_j = T_a + P × R_th, from the ambient temperature T_a, the dissipated power P and the total junction-to-ambient thermal resistance R_th (°C/W). The result, in °C, is the device's internal temperature (silicon junction), which must not exceed the manufacturer's limit (typically 150 °C) on pain of failure. The thermal resistance adds the junction-to-case, case-to-heatsink and heatsink-to-ambient stages. Lowering R_th (larger heatsink, ventilation, thermal paste) lowers the junction temperature. It is the central calculation of power electronics thermal design. Enter the ambient temperature, the dissipated power and the thermal resistance.
Fillet Weld Throat
Calculate the effective throat of a fillet weld, a = 0.707 × z, from the leg z of the fillet. For an equal-leg fillet, the throat — the smallest dimension of the resisting section, from root to face — equals the leg times sin(45°) ≈ 0.707. The result, in the same unit as the leg (mm), is the dimension used to calculate the strength of the welded joint, since the weld tends to fail across this minimum section. Sizing the throat correctly ensures the weld carries the design load. Enter the fillet leg.
Bolt Shear Stress
Calculate the shear stress in transversely loaded bolts, τ = F ÷ (n·A), from the total shear force F (N), the number of bolts (or shear planes) n and each bolt's area A (mm²). Unlike tensioned joints (where the bolt is tightened and the load is axial), in SHEAR joints the bolts resist a transverse force tending to slide one part over another (as in steel structural connections, splice plates, flanges under lateral load). The force is distributed among the bolts and each works in shear — hence the stress is force divided by the number of bolts times the area. There can be SINGLE shear (one shear plane) or DOUBLE shear (two planes, when the bolt passes through three plates), doubling capacity. The area used depends on whether the shear plane passes through the threaded part (use the tensile area) or the smooth shank (nominal-diameter area). Shear stress is compared with the bolt material's shear strength (typically ~0.6 of tensile strength). In structures, bearing-type (bolt in shear/bearing) and slip-critical (preload friction transmits load without bolt shear) connections are distinguished — this formula covers shear resistance. Enter the shear force, the number of bolts and the area.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.