Deflection Calculation
Deflection is the displacement of a beam under load. Common methods for calculating deflection include double integration, moment-area method, and superposition. The differential equation is EI × d²y/dx² = M(x). Deflections are important for serviceability (user comfort) and to prevent excessive deformation.
Knowledge Check
1.What is the maximum deflection for a simply supported beam with a point load P at midspan?
2.A simply supported beam with UDL has a maximum deflection of 10 mm. If the load is doubled, what is the new deflection?
3.In the beam deflection equation EI × d²y/dx² = M(x), what does 'EI' represent?
4.A cantilever beam with a point load P at the free end has a maximum deflection at the free end given by:
5.What is the maximum deflection of a simply supported beam with UDL w over length L?
6.The principle of superposition can be used to find deflections if the beam is:
7.A cantilever beam of length 3 m has a UDL of 10 kN/m. If E = 200 GPa and I = 50×10⁶ mm⁴, what is the free end deflection?
8.In the double integration method, the first integration of the moment equation gives:
9.A beam with greater flexural rigidity (EI) will have:
10.What is the maximum deflection at the free end of a cantilever with a point load at midspan?