Calculations Received

As promised the missing sheet of beam calculations was eMailed to me this morning. It seems to involve using the loading figures for a standard floor and ceiling to calculate two values. One of these is the 'Z' value which seems to be some kind of volume (cubic mm). It is calculated using the Maximum Bending Moment of the beam, which is a function of the beam load, and also increases by the square of it's length. The other calculated value is the beam deflection at it's centre point.

A colleague from work who trained as a civil engineer helped me out with this. There is a simple formula for calculating the maximum permissable deflection, which is in direct proportion to the beam length (L/360). A more complex calculation gives the actual deflection of the beam. This uses the loading values plus figures from the beam specification, along with the "Youngs Modulus" of steel which is something I remember vaguely from the "Properties of Materials" lectures in my days as a Physics student.

Despite not understanding them completely, I reproduced the calculations in a spreadsheet and came to the same answers, which gave me a little confidence. Better than this, I was able to vary the length of the beam to see at what point is becomes under-specified. The existing calculations are for a 5.55m beam. It looks to me like the limit is 6.3m, after which the 'Z' value goes out of spec. At 6.37m the allowable deflection is also exceeded.

Looking at the plans I think we are going to need a length of just under 7m, so I think a beam upgrade is on the cards. The builder thinks we will probably just need the next grade higher. This is not a physically bigger beam, just made of thicker metal, so it should be a like-for-like replacement. It looks like I will need the calculations to be professionally done though. I doubt the building inspector will accept my amateur spreadsheet.