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Moment-curve equation. #els-crv

Elastic curve governing equation.

- Find the bending moment \( M(x) \).
- Integrate both sides of the governing equation twice.
- Solve for \( y(x) \).

- \( y(x) \) is the vertical direction
- Bending only: we will neglect effects of transverse shear
- Small deflection angles

Elastic curve equation for constant E and I.

Differentiating the elastic curve equation.

Differentiating the elastic curve equation a second time.

- \( EIy''(x): \) bending moment
- \( EIy '''(x): \) shear force
- \( EIy''''(x): \) distributed load

Shear force.

Internal bending moment.

Slope of the tangent line.

Deflection.

- \( y(x): \) deflection
- \( y'(x): \) slope

Example: Overhanging beam. #ovr-hng

Example: Cantilever beam. #can-tlv

Taken from the formula sheet

Example: Deflection from a moment and distributed load using superpositon. #dfl-spp