Found by integrating EI y''=M or by tables and superposition.
The elastic curve satisfies EI·d²y/dx²=M(x). Integrating twice gives slope and deflection with boundary conditions. Standard cases: cantilever with end load δ=PL³/(3EI); simply supported UDL δ=5wL⁴/(384EI).
A 2 m steel cantilever with EI=1 MN·m² and 1 kN tip load deflects 2.7 mm.
Deflection controls serviceability, because a floor that bends too much feels unsafe or cracks finishes even if it does not fail.
Found by integrating EI y''=M or by tables and superposition.
Deflection controls serviceability, because a floor that bends too much feels unsafe or cracks finishes even if it does not fail.
A limit on deflection, vibration or cracking that affects comfort or function, rather than the strength that prevents collapse.
Use standard tables for common load and support cases, or superposition of simple cases for combined loading.
Typical applications include checking the sag of a floor beam against the span-over-360 limit, predicting the tip deflection of a cantilever balcony and designing a crane runway so the rail stays straight under load.
Study "Section modulus" first (topic 56 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Deflection limits like L/360. Superposition for multiple loads. Macaulay method handles point loads.
A 2 m steel cantilever with EI=1 MN·m² and 1 kN tip load deflects 2.7 mm.
The next topic is "Statically indeterminate beams", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 57 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.