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.
Result
—
Timber Design Strength from k_mod Factors (NBR 7190)
When checking a timber member at the ultimate limit state, the tabulated value of the strength class never enters the calculation directly. Between the characteristic strength in the table and the resisting stress compared against the design action sit four numbers: three modification factors and the material partial safety factor. Getting one of them wrong shifts the whole sizing of a purlin or a shed column. This page handles that step: enter k_mod1, k_mod2, k_mod3, the characteristic strength and γ_w, and it returns the design strength in MPa.
The calculation is f_d = k_mod1 · k_mod2 · k_mod3 · f_k / γ_w. The k_mod1 factor covers load duration — timber being the common structural material that loses strength under sustained load, the factor runs from 1.10 for instantaneous action down to 0.60 for permanent load. The k_mod2 factor covers the service moisture class and k_mod3 the timber grade. With the page defaults — 0.70, 1.00, 1.00, f_k = 40 MPa and γ_w = 1.4 — the output is 20.00 MPa, exactly half of f_k, since 0.70/1.4 = 0.5. Switch to permanent load and it reads 17.14 MPa; instantaneous action gives 31.43 MPa; dropping k_mod2 to 0.80 gives 16.00 MPa.
The page carries no code tables: it multiplies whatever you type. The only filter is the accepted range — modification factors up to 1.20 and γ_w between 1 and 3 — so a k_mod copied from the wrong row slips through unnoticed. Check which edition of the standard governs your project, since the load-duration table and the list of moisture classes shifted between revisions, and one formulation uses two factors instead of three: in that case enter 1.00 in the remaining field. Finally, f_d is a strength, not a verification: comparing it with the design stress of the combination and handling stability separately remains your job. Deflection follows another route, through the effective modulus.
Frequently asked questions
Why does the design strength come out at exactly half the characteristic value?
Which partial safety factor γ_w should I use?
Does the tool include the k_mod tables?
Related Tools
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.
Number of Lanes Required
Calculate the number of lanes required on a road, N = V ÷ C_lane, dividing the design traffic volume V by the capacity of one lane C_lane (vehicles/h per lane). The result is the minimum number of lanes to serve the demand within capacity; in practice, always round up to the next integer. It is a basic sizing calculation in the geometric design of highways and urban roads, defining the cross-section from the predicted volume and the per-lane capacity (which depends on speed, road type and traffic conditions). Enter the traffic volume and the per-lane capacity.
Buller-Woodrow Loss Factor
Estimates the loss factor of a distribution feeder from its load factor using the empirical Buller-Woodrow relation: loss factor = k × load factor + (1 − k) × load factor squared. The loss factor is the ratio of average loss to peak loss over the period, and it is what turns the instantaneous loss measured at peak hour into energy lost over the month without needing a recorded load curve. Because Joule loss varies with the square of the current, the loss factor always sits below the load factor, and the lower the load factor the lower the ratio between them: at a load factor of 0.20 the loss factor is under half of it, while at 0.80 it sits around 86% of its value. The coefficient k is an input rather than fixed at 0.30, the classic Buller-Woodrow value for distribution networks, because utilities recalibrate k between 0.15 and 0.50 according to the feeder load profile. Enter the load factor for the period and the coefficient k.
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.
Number of Stages by the Gilliland Correlation
Estimates the number of theoretical stages of a distillation column with the Gilliland correlation, which links excess reflux to excess stages: with X = (R − R_min)/(R + 1) and Y = (N − N_min)/(N + 1), you get N = (Y + N_min)/(1 − Y). It is the third step of the FUG shortcut method, after N_min from the Fenske equation and R_min from Underwood, and it settles in one line the preliminary sizing that would otherwise need a McCabe-Thiele diagram or a simulator. Eduljee's analytical fit is adopted, Y = 0.75·(1 − X^0.5668), the usual form for hand calculation; the Molokanov correlation is more accurate at the extremes and gives a result a few percent different. Enter the operating reflux ratio, the minimum reflux ratio and the minimum number of stages.
Axle Load Equivalency Factor
Computes how many passes of the standard axle are equivalent to one pass of the real axle, using the power law of pavement design: factor = (axle load ÷ standard axle load) raised to the damage exponent. This factor is what converts a traffic count into the number N of standard axle repetitions, which in Brazil is the 8.2 tf, or 80 kN, single axle with dual wheels. The exponent amplifies overload brutally: an axle 20% heavier than the standard does not consume 20% more pavement but 2.07 times as much, which is why a single overloaded truck weighs more on the life of the road than thousands of cars, whose factor is practically zero. The exponent is an input rather than fixed at 4, the AASHTO value known as the fourth power law, because rigid pavement and fatigue cracking models work with exponents between 3 and 5 and the result shifts by a whole level depending on the choice. Enter the axle load, the standard axle load and the damage exponent.
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.