beamZ

beamZ

formulas

point loads

δ = FL^3 ∕ 48EI    -  see   http://www.clag.org.uk/beam.html

where

L = length of beam

δ = deflection of beam

F = force

E = Young's Modulus

I = moment of inertia of beam

for uniformly 

distributed loads of w N/m

δ = 5wL^4 ∕ 384EI

moment of inertia I

                                          rectangular beam

       
I = bh^3/12

more complicated shapes can be solved by 

negative area method 
or

parallel axis theorem    
I = Sum(Ii + Aidi^2

where the shape is split into simpler elements each with area Ai offset di from centroid

example
                                                   RHS

by negative area method

IRHS = BH^3/12 - bh^3/12

where RHS has uniform thickness t = (B-b)/2 = (H-h)/2

universal I beam can be done similar way or by parallel axis theorem

Materials properties

               elasticity E       max stress           density                 note

timber      10 GPa          30 - 70 MPa        500 Kg/m^3     MGP10 H3 exterior                                                            
steel         200 GPa           450 MPa          7850 Kg/m^3

for steel beam properties go to http://www.steelweb.info/200UB22.htm

concrete   - max single span L = 15 h for beam
                                                 30 h for slab

see also  http://www.concrete.net.au/publications/pdf/Long-span Floors.pdf