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curved beams
- Thread starter zipper2
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The formula for bending stress in a curved beam is:
σ = (M*y)/(A*e*(r+y))
where: M - bending moment, y - distance from the neutral axis to the point where we calculate the stress, A - cross-sectional area, e = r_c - r - distance from the neutral axis to the centroid, r_c - distance from the center of curvature to the centroid of the cross section, r - distance from the center of curvature to the neutral axis (different formulas for each section, general equation is with integral).
Usually we also add normal stress from axial force to this equation using the principle of superposition so the equation becomes:
σ = (P/A) + ((M*y)/(A*e*(r+y)))
where: P - axial force
Displacements can be calculated using the Castigliano's theorem.
σ = (M*y)/(A*e*(r+y))
where: M - bending moment, y - distance from the neutral axis to the point where we calculate the stress, A - cross-sectional area, e = r_c - r - distance from the neutral axis to the centroid, r_c - distance from the center of curvature to the centroid of the cross section, r - distance from the center of curvature to the neutral axis (different formulas for each section, general equation is with integral).
Usually we also add normal stress from axial force to this equation using the principle of superposition so the equation becomes:
σ = (P/A) + ((M*y)/(A*e*(r+y)))
where: P - axial force
Displacements can be calculated using the Castigliano's theorem.
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