Final Prestressing Force
Calculate the final (effective) prestressing force after losses, P_∞ = P_0·(1 − losses/100), from the initial prestressing force P_0 (kN) and the total loss percentage (%). A member's prestressing force is NOT constant: it starts at an initial value (the jacking force) and DECREASES due to the various losses — immediate (elastic shortening, friction, anchorage set) and time-dependent (concrete shrinkage and creep, steel relaxation). The effective final force, after all losses stabilize (after years), is what actually acts in the structure in service and must ensure performance. Total losses typically sum 15-25% of the initial force in post-tensioned structures and can reach 20-30% in pretensioned ones. This simple calculation applies the total loss percentage to the initial force, giving the effective force — fundamental to check service stresses, cracking and member deflection. The designer works with TWO critical situations: maximum INITIAL force (right after transfer, member still unloaded — risk of excess compression or top-fiber tension) and minimum FINAL force (after all losses, member loaded — risk of decompression and cracking). Enter the initial force and the total loss percentage.
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Força de protensão final
A força de protensão final (efetiva) após as perdas é P_∞ = P_0·(1 − perdas/100), a partir da força de protensão inicial P_0 e do percentual total de perdas. A força de protensão de uma peça não é constante: ela parte de um valor inicial (a força aplicada pelo macaco) e diminui por causa das diversas perdas — as imediatas (encurtamento elástico, atrito, acomodação da ancoragem) e as diferidas ao longo do tempo (retração e fluência do concreto, relaxação do aço). A força final efetiva, depois de todas as perdas se estabilizarem (após anos), é a que realmente atua na estrutura em serviço e deve garantir o desempenho. As perdas totais somam tipicamente 15 a 25% da força inicial em estruturas pós-tracionadas e podem chegar a 20 a 30% em pré-tracionadas. Este cálculo aplica o percentual total de perdas à força inicial, dando a força efetiva — fundamental para verificar as tensões em serviço, a fissuração e a flecha. O projetista trabalha com duas situações críticas: a força inicial máxima (logo após a protensão, com a peça ainda descarregada — risco de excesso de compressão ou tração na fibra superior) e a força final mínima (após todas as perdas, com a peça carregada — risco de descompressão e fissuração). Informe a força inicial e o percentual total de perdas.
Related Tools
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.
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.
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.
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.