Building Construction Handbook, Eighth Edition

Simple beam design (Deflection)

The deflection due to loading, other than the weight of the

structure, should not exceed 1/360 of the span.

The formula to determine the extent of deflection varies,

depending on:-

(a) Point loading

(b) Uniformly distributed loading

where: W = load in kN

L = span in cm

E = Young's modulus of elasticity (typically 21,000 kN/cm^2

for steel)

I = 2nd moment of area about the x-x axis (see BS 4-1)

Using the example of 200 kN uniformly distributed over a 4 m

span:-

Deflection =5WL

3

384EI=

(^5) ¾ (^200) ¾ (^43) ¾ 1003
(^384) ¾ (^21000) ¾ 9504 = 0„835cm
Permissible deflection is 1/360 of 4 m = 11„1 mm or 1„11 cm.
Therefore actual deflection of 8„35 mm or 0„835 cm is acceptable.
Ref. BS 5950-1: Structural use of steelwork in building. Code of
practice for design. Rolled and welded sections.
Structural Steelwork---Beam Design (3)