True Stress
Calculate the true stress, σ_t = s × (1 + e), from the engineering stress s (MPa) and the engineering strain e. Engineering stress uses the specimen's initial area, but during a tensile test the real cross-section shrinks; true stress corrects this using the instantaneous area (assuming constant volume in the uniform region), always giving a higher value than engineering stress. It is essential to build the true stress-strain curve and model strain hardening (σ = K·εⁿ). The result is in the same unit as the input stress. Enter the engineering stress and strain.
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True stress
The engineering stress read from a tensile test is the force divided by the initial cross-sectional area of the specimen (s = F/A₀). The problem is that as the material stretches, the cross-section shrinks — so the initial area understates the stress the material actually feels. True stress corrects this by using the instantaneous area: σ_v = F/A. Assuming the volume is conserved in the region of uniform deformation (A·L = A₀·L₀), one arrives at the practical relation σ_v = s × (1 + e), where e is the engineering strain. Since (1 + e) is always greater than 1, true stress is always higher than engineering stress, and the difference grows with strain. The true stress-strain curve is the one that reveals the material's physical behavior: unlike the engineering curve (which 'drops' past the maximum stress because of necking), the true curve keeps rising, showing that the material keeps strain-hardening. In the uniform plastic region it usually follows the power law σ = K·εⁿ, where n is the strain-hardening exponent. Enter the engineering stress and strain.
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True Strain
Calculate the true (logarithmic) strain, ε = ln(1 + e), from the engineering strain e (dimensionless or fractional). While engineering strain uses the fixed initial length as reference, true strain integrates the instantaneous length changes, being additive and better suited to large plastic deformations such as in metal forming (rolling, extrusion, drawing). The result is the actual strain accumulated by the material. For small strains, ε ≈ e; the difference grows as strain increases. Enter the engineering strain.
Bolt Tensile Stress
Calculate the tensile stress in a bolt, σ = F_b ÷ A_t, from the total bolt tensile force F_b (N) and the tensile stress area A_t (mm²). It is the basic strength check of a tensioned bolt: the acting stress (force over resisting area) must be below the material strength with a safety margin. The force F_b is the total load the bolt carries — in a preloaded joint, the preload plus the fraction of external load reaching the bolt (F_i + C·P). The resulting stress is compared with the proof strength S_p (the limit up to which the bolt can be loaded without permanent deformation — typically 85-90% of yield) or the ultimate strength, per the criterion. The bolt strength class (marked on the head: 8.8, 10.9, 12.9 metric; or SAE grades 2, 5, 8) sets these allowable stresses — a class 8.8 bolt has a proof strength of 580-600 MPa, a 12.9 reaches ~970 MPa. Verifying σ does not exceed the allowable, considering preload and service load, is essential: overloaded bolts yield (losing preload) or break. With the fatigue and separation checks, it defines the tensioned joint's safety. Enter the total bolt force and the tensile area.
Percent Elongation
Calculate the percent elongation, A% = (L_f − L₀) ÷ L₀ × 100%, from the initial gauge length L₀ and the final length L_f measured after rupture in a tensile test (fitting the two halves of the specimen back together). The result, in %, is a direct measure of the material's ductility — how much it stretches before breaking. Ductile steels reach 20–40%; brittle materials, a few percent. Elongation depends on the gauge length used, so it is always quoted with it (e.g. A% over 50 mm). Enter the initial and final lengths.
Bolt Tensile Stress Area (Metric)
Calculate the tensile stress area of a metric-thread bolt, A_t = (π/4)·(d − 0.9382·p)², from the nominal diameter d (mm) and the thread pitch p (mm). The tensile stress area is the EFFECTIVE cross-section resisting tension in a threaded bolt — and it is NOT the nominal-diameter area (the smooth cylinder) nor the root-diameter area (the thread bottom). Because of the helical thread geometry, tensile rupture occurs at an intermediate section, and tests showed it corresponds to an effective diameter equal to the average of the pitch and root diameters, leading to the formula with the 0.9382·p term (a geometric constant of the ISO metric thread, 60° triangular profile). The tensile area is the fundamental parameter for all bolt strength calculations: preload, tensile stress, proof load and ultimate strength are all found by multiplying A_t by the corresponding material stress. Using the wrong area (the larger nominal-diameter one) would overestimate strength and lead to undersized joints. Bolt tables list A_t for each diameter-pitch combination; this formula computes it for any metric thread. Enter the nominal diameter and the thread pitch.
Percent Cold Work
Calculate the percent cold work (area reduction), %CW = (A₀ − A_f) ÷ A₀ × 100%, from the initial cross-section area A₀ and the final area A_f after cold plastic deformation (rolling, drawing, stamping). The result, in %, shows how much the material was deformed below the recrystallization temperature. Cold work strain-hardens the metal: it raises the yield strength and hardness and lowers ductility as dislocations multiply and tangle. It is the parameter used to control properties before an anneal. Enter the initial and final areas.
Geosynthetic Tensile Stiffness
Calculate a geosynthetic's tensile stiffness (secant stiffness modulus), J = T ÷ ε, from the tensile force per unit width T (kN/m) and the corresponding strain ε (dimensionless, or ε/100 if in %); the result, in kN/m, is the stiffness. Unlike conventional materials, where stiffness is Young's modulus (stress/strain, in Pa), in geosynthetics the 'stress' is expressed per unit WIDTH (kN/m, since thickness is ill-defined and variable), so the stiffness J is also in kN/m. Tensile stiffness is fundamental in soil reinforcement design because geosynthetics only mobilize force when they DEFORM (stretch): the higher the stiffness J, the smaller the deformation needed to reach the required reinforcement force. This is crucial because reinforced-soil structures have ALLOWABLE deformation limits (a wall cannot bulge too much, an embankment cannot settle excessively) — so design is often controlled by stiffness (deformation) rather than strength (rupture). Modern reinforcement geosynthetics (polyester or HDPE geogrids) have high stiffness to limit deformations. Stiffness is measured in the wide-width tensile test, usually at a reference strain (2%, 5%). Enter the tensile force and the strain.
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.