Initial Prestress Stress
Calculate the allowable initial stress in prestressing steel, σ_pi = coef·f_ptk, from the code coefficient (fraction of strength) and the steel characteristic tensile strength f_ptk (MPa). Prestressing steel is tensioned to a VERY HIGH stress — a significant fraction of its tensile strength — possible because these are HIGH-STRENGTH steels (strands with f_ptk of 1900 MPa, versus ~500 MPa for ordinary reinforcing steel). But there is a LIMIT to the initial stress, set by code for safety and to limit relaxation: typically the lesser of about 0.74·f_ptk and 0.82·f_pyk (yield strength) for low-relaxation steels in pretensioning, with slightly different values for post-tensioning and right after anchorage. Applying a high initial stress is DESIRABLE (more effective prestress, less steel needed), but the code limit prevents tensioning the steel too close to yield (which would reduce safety margin and greatly increase relaxation). This calculation gives the jacking stress to apply (before losses), the starting point of all prestress design. Enter the code coefficient and the steel characteristic strength.
Resultado
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Tensão inicial de protensão
A tensão inicial admissível na armadura de protensão é σ_pi = coef·f_ptk, a partir do coeficiente normativo (fração da resistência) e da resistência característica à ruptura do aço f_ptk. O aço de protensão é tracionado a uma tensão muito alta — uma fração significativa de sua resistência à ruptura —, o que é possível porque são aços de alta resistência (cordoalhas com f_ptk de 1900 MPa, contra ~500 MPa do aço de concreto armado comum). Mas há um limite para a tensão inicial, prescrito por norma para garantir segurança e limitar a relaxação: tipicamente a menor entre cerca de 0,74·f_ptk e 0,82·f_pyk (resistência ao escoamento) para aços de relaxação baixa na pré-tração, com valores ligeiramente diferentes para pós-tração e para o instante após a ancoragem. Aplicar uma tensão inicial alta é desejável (mais protensão efetiva, menos aço necessário), mas o limite normativo impede tracionar o aço perto demais do escoamento (o que reduziria a margem de segurança e aumentaria muito a relaxação). Este cálculo dá a tensão de tracionamento que o macaco deve aplicar (antes das perdas), ponto de partida de todo o dimensionamento da protensão. Informe o coeficiente normativo e a resistência característica do aço.
Related Tools
Steel Relaxation Loss
Calculate the prestress loss from steel relaxation, Δσ = (ψ/100)·σ_pi, from the relaxation coefficient ψ (% of initial stress) and the initial tendon stress σ_pi (MPa). Relaxation is a STEEL phenomenon analogous to concrete creep: when a steel wire or strand is held under CONSTANT tension (fixed elongation, as in an anchored prestressing tendon), its stress DECREASES slowly over time, even without length change. It is as if the steel 'yields' microscopically under prolonged load, losing part of its tension. Relaxation depends on the steel type (LOW-relaxation steels — LR —, thermomechanically treated, relax much less, ~2.5% in 1000h at 0.7·fptk, than normal-relaxation — NR —, ~12%), the initial stress level (the higher, the more relaxation) and temperature. The coefficient ψ is tabulated as a function of these factors and time. Relaxation is one of the TIME-DEPENDENT prestress losses, along with concrete shrinkage and creep, and design sums them all for the total loss and the effective final prestressing force. Enter the relaxation coefficient and the initial tendon stress.
Elastic Shortening Loss
Calculate the prestress loss from concrete elastic shortening, Δσ = (E_s/E_c)·σ_c, from the steel modulus E_s (MPa), the concrete modulus E_c (MPa) and the concrete stress at the tendon level σ_c (MPa). It is one of the IMMEDIATE prestress losses (at transfer, not over time): when the tendon is tensioned and anchored, it compresses the concrete, and the concrete, being compressed, SHORTENS elastically. Since the tendon is bonded or anchored in this shortened concrete, it shortens too — and shortening, it LOSES part of its tension. The loss is proportional to the modular ratio αe = E_s/E_c (typically 6-8, since steel is much stiffer than concrete) times the concrete compression stress at the tendon level. In members with SEVERAL tendons prestressed sequentially, each new tendon compresses and shortens the concrete, causing loss in already-anchored tendons — so the average loss is often taken as half the value (the first tendons lose more than the last). This is one of the losses to subtract from the initial force to get the effective prestressing force. Enter the steel and concrete moduli and the concrete stress.
Edge Stress from Prestressing
Calculate the normal stress at an extreme fiber of a prestressed concrete section, σ = P/A + (P·e)/W, from the prestressing force P (MN), the section area A (m²), the tendon eccentricity e (m) and the section modulus W (m³). Prestressed concrete is one of the great structural engineering inventions of the 20th century: high-strength steel tendons are tensioned (prestressed) and anchored in the member, COMPRESSING the concrete before it even receives service loads. Since concrete is strong in compression but weak in tension, this pre-compression 'cancels' the tensions external loads would cause, allowing much longer spans and slenderer members than conventional reinforced concrete. The tendon is placed with ECCENTRICITY (below the centroid), so prestressing generates not only uniform compression (P/A) but also a moment (P·e) producing stresses opposite to the loading — compressing exactly the fiber that would tend to crack. This formula computes the resulting edge stress, summing axial compression and prestress bending; design verifies stresses stay within limits in all phases (at transfer, empty, and in service, loaded). Enter the prestressing force, area, eccentricity and section modulus.
Cable Tension in Accelerated Lift
Calculate the dynamic tension in a cable while lifting a load with acceleration, T = W·(1 + a/g), from the load weight W (N), the vertical lift acceleration a (m/s²) and gravity g. When a load is lifted with ACCELERATION (at lift start, when accelerating the rise), the cable must provide not only the force to support the weight (W) but ALSO the force to accelerate the mass upward — by Newton's second law, the total tension is the weight times the factor (1 + a/g). This means the DYNAMIC tension is GREATER than the static weight: an acceleration of g/2 (5 m/s²) raises the tension by 50%! That is why ABRUPT lifts (fast start, or worse, lifting an already-moving load or stopping abruptly) generate dangerous dynamic OVERLOADS in the cable, which can break it even with the static load within capacity. The effect is worse in abrupt STOPS and in loads 'snatching off the ground' (cable slack suddenly removed, generating an impact). So experienced operators lift SMOOTHLY (low acceleration), and the cable safety factors (5 or more) exist precisely to cover these inevitable dynamic overloads. This calculation quantifies the tension increase due to acceleration, essential in the safety analysis of dynamic lifts. Enter the load weight and the lift acceleration.
Admissible Stress for Steel and Concrete
Computes admissible stress for steel and concrete given characteristic strength and safety factor.
Kern Distance
Calculate the kern distance of a section, c = W/A, from the section modulus W (m³) and the section area A (m²). The kern is a central region of the cross-section with a remarkable property: if a COMPRESSION force (like prestress, or a column load) is applied WITHIN the kern, the whole section stays compressed (no fiber tensions); if the force leaves the kern, tensions appear on the opposite edge. The kern distance is the boundary: for a rectangular section, the kern is the famous 'middle third' (the force must fall in the central third of the height to avoid tension). The distance c = W/A defines how far the eccentricity can go while keeping the section fully compressed. This concept is central in three areas: in PRESTRESSING (the tendon eccentricity is chosen considering the kern, to control edge stresses in each loading phase), in FOUNDATIONS and COLUMNS (the load resultant must fall in the kern so the base does not 'lift off' the soil, avoiding tension — the middle-third rule for footings), and in gravity wall and dam stability. Knowing the kern is essential for tendon placement and stress checks in eccentrically compressed members. Enter the section modulus and the section 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.