For my question, I am following a previous method I used in my HNC where I had to determine the position and magnitude of the maximum bending moment. I am now working on my project and I have revisited this question but I am having some issues in my method. The above diagram is of a simply supported structure with the weight of an average cat in the centre. The structure is 500mm wide and simply supported at either end as shown.
The cat weighs 4.5kg which translates to a force of 44.2N and as it is stood in the centre of the structure (250mm), R1 and R2 must react with 22.1N to maintain the structure.
Therefore my first answer is below in FIG 1.
Next I introduced Snow to the structure giving s uniform distributed load across.
I worked out that, typically snow weighs between 70kg and 150kg per cubic meter. I have a surface area of 500mm x 500mm with a possible depth of 150mm snow on the structure. Therefore, the cubic area would be
Which leads me to my next diagram as shown below.
This time due to the snow fall on the roof, the reactive force from R1 and R2 must compensate for the additional weight. This method is shown in FIG 2.
I cannot see how the maximum bending moment in both situations much less than the force from the cat alone. I have tried this several ways and ended up with different answers each time. I believe my error is in the units of measurment as I am showing my answer in N m and the structure is only 500mm or 0.5m wide. Should I show my answer in N mm? am I making another error somewhere along the way?
All my methods are below.
The Attempt at a Solution