Concrete Shrinkage Loss
Calculate the prestress loss from concrete shrinkage, Δσ = ε_cs·E_s, from the shrinkage strain ε_cs (dimensionless) and the steel modulus E_s (MPa). Shrinkage is the volume reduction concrete undergoes over time as it LOSES water by evaporation (drying shrinkage) and through cement hydration reactions (autogenous shrinkage), independent of loading. When the concrete of a prestressed member shrinks (shortens), the bonded steel tendon shortens too — and shortening, it LOSES tension, exactly as in elastic-shortening loss, except here the shortening is from shrinkage and occurs SLOWLY over months and years. The loss is simply the shrinkage strain times the steel modulus (the stress that shortening 'steals' from the tendon). The shrinkage strain ε_cs is typically 0.0002-0.0005 (200-500 microstrains) and depends on ambient humidity (drier = more shrinkage), member dimensions (thin members shrink more, losing water faster), mix and time. It is one of the three time-dependent losses (with creep and relaxation) reducing prestress over the structure's life. Enter the shrinkage strain and the steel modulus.
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Perda por retração do concreto
A perda de protensão por retração do concreto é Δσ = ε_cs·E_s, a partir da deformação específica de retração ε_cs e do módulo de elasticidade do aço E_s. A retração é a redução de volume que o concreto sofre ao longo do tempo conforme perde água por evaporação (retração por secagem) e pelas reações de hidratação do cimento (retração autógena), independentemente de carregamento. Quando o concreto de uma peça protendida retrai (encurta), o cabo de aço aderido a ele encurta junto — e ao encurtar, perde tração, exatamente como na perda por encurtamento elástico, só que aqui o encurtamento é por retração e ocorre lentamente ao longo de meses e anos. A perda é simplesmente a deformação de retração vezes o módulo do aço (a tensão que esse encurtamento 'rouba' do cabo). A deformação de retração ε_cs é tipicamente da ordem de 0,0002 a 0,0005 (200 a 500 microstrains) e depende da umidade ambiente (mais seco = mais retração), das dimensões da peça (peças finas retraem mais, pois perdem água mais rápido), do traço e do tempo. É uma das três perdas diferidas (com fluência e relaxação) que reduzem a protensão ao longo da vida da estrutura. Informe a deformação de retração e o módulo de elasticidade 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.
Concrete Creep Loss
Calculate the prestress loss from concrete creep, Δσ = φ·(E_s/E_c)·σ_cg, from the creep coefficient φ (dimensionless), the modular ratio E_s/E_c and the concrete stress at the tendon level from permanent loads σ_cg (MPa). Creep is the SLOW, growing deformation concrete undergoes under CONSTANT load over time: besides the immediate elastic shortening when compressed, concrete keeps shortening gradually for months and years, reaching a total deformation 2-3 times the initial elastic one. In a prestressed member, the concrete is PERMANENTLY compressed by the prestress, so it creeps (shortens slowly), and the bonded tendon shortens with it, LOSING tension — the largest time-dependent loss in many cases. The loss is the creep coefficient φ (typically 1.5-3.5, a function of humidity, loading age, member dimensions) times the equivalent elastic loss (modular ratio × concrete stress). With shrinkage and relaxation, creep defines the total time-dependent prestress loss. Estimating these losses well is crucial: underestimating leaves the member with less prestress than intended (cracking risk); overestimating wastes steel. Enter the creep coefficient, the modular ratio and the concrete 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.
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.