Balkteori

Balkteori is the area of structural theory that studies how beams respond to loads through bending, including the resulting deflections, internal bending moments, and shear forces. It provides mathematical models that allow engineers to predict how slender structural elements behave under various loading conditions.

The classical model is the Euler-Bernoulli beam theory. It assumes slender beams, small deflections, material linearity and isotropy, and that cross-sections remain plane and perpendicular to the beam axis after deformation. In this theory the transverse deflection w(x) is related to the distributed load q(x) by the beam equation E I d^4w/dx^4 = q(x), where E is Young’s modulus and I is the second moment of area of the cross-section. The bending moment M(x) is related to curvature by M = -E I d^2w/dx^2, and the shear force V(x) = dM/dx. This framework yields solutions for common beam configurations, supports, and loading schemes, allowing the determination of deflections, rotations, and internal forces.

A more general model is the Timoshenko beam theory, which adds shear deformation and rotational inertia to address thick or short beams where the Euler-Bernoulli assumptions are less accurate. In practice, engineers choose the appropriate theory based on beam geometry, material, and expected deformations.

Balkteori underpins much of civil, mechanical, and aerospace engineering, informing design of buildings, bridges, machine components, and structural systems. Its limitations include the assumption of linear elasticity, small deflections, and, in basic form, negligible shear effects.