Prestress Moment
Calculate the moment generated by eccentric prestressing at a section, M_p = P·e, from the prestressing force P (kN) and the tendon eccentricity e (m). When the prestressing tendon is positioned with ECCENTRICITY relative to the section centroid (usually below, in the region tensioned by loads), the prestressing force, besides axially compressing the section (P/A), generates a BENDING MOMENT equal to force times eccentricity. This prestress moment is the key to prestressed concrete's efficiency: it is OPPOSITE to the moment from external loads (self-weight, live loads), 'bowing' the member upward (camber) and producing top-fiber tension and bottom-fiber compression — exactly the opposite of what the load does. So eccentric prestressing 'pre-loads' the member against the service loading, so that when loads act, they must first CANCEL the prestress effects before tensioning the concrete. That is why prestressed beams often show camber (upward curvature) when still unloaded. The prestress moment is fundamental in computing edge stresses, camber and the optimal tendon profile along the member (which roughly follows the load moment diagram, with varying eccentricity). Enter the prestressing force and the eccentricity.
Resultado
—
Momento de protensão
O momento gerado pela protensão excêntrica em uma seção é M_p = P·e, a partir da força de protensão P e da excentricidade do cabo e. Quando o cabo de protensão é posicionado com excentricidade em relação ao centroide da seção (geralmente abaixo, na região tracionada pelas cargas), a força de protensão, além de comprimir axialmente a seção (P/A), gera um momento fletor igual ao produto da força pela excentricidade. Esse momento de protensão é a chave da eficiência do concreto protendido: ele é oposto ao momento causado pelas cargas externas (peso próprio, sobrecargas), 'curvando' a peça para cima (contraflecha) e produzindo trações na fibra superior e compressões na inferior — exatamente o contrário do que a carga faz. Assim, a protensão excêntrica 'pré-carrega' a peça de forma contrária ao carregamento de serviço, de modo que, quando as cargas atuam, elas primeiro precisam anular os efeitos da protensão antes de tracionar o concreto. É por isso que vigas protendidas frequentemente exibem uma contraflecha (curvatura para cima) quando ainda descarregadas. O momento de protensão é fundamental no cálculo das tensões nas bordas, da contraflecha e do traçado ótimo do cabo ao longo da peça (que segue aproximadamente o diagrama de momentos das cargas, com excentricidade variável). Informe a força de protensão e a excentricidade.
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.
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.
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.
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.