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.
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Kern distance
The kern distance of a cross section is c = W/A, obtained from the section modulus W and the cross-sectional area A. The kern (also called the core) is a central region of the cross section with a remarkable property: if a compressive force (such as a prestressing force, or the load carried by a column) is applied inside the kern, the whole section stays in compression and no fibre goes into tension; if the force falls outside the kern, tensile stresses appear at the opposite edge. The kern distance is exactly that boundary: for a rectangular section the kern is the well-known 'middle third' (the force must land within the central third of the depth to avoid tension). The distance c = W/A therefore defines how far the eccentricity may go while the section remains fully compressed. The concept is central to three fields: prestressing (tendon eccentricity is chosen with the kern in mind, to keep edge stresses under control at every stage); foundations and columns (the resultant of the loads must land inside the kern so the base does not lift off the soil, avoiding tension — the middle-third rule for spread footings); and the stability of retaining walls and gravity dams. Knowing the kern is essential for laying out tendons and for checking stresses in eccentrically compressed members. Enter the section modulus and the cross-sectional area.
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.
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.
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