Why is the maximum cooling load not the same as the sum of the internal and solar gains?

It isn't possible to calculate summer design cooling loads for each hour by simply summing internal gains for that hour because it is necessary to take into account the building thermal mass, as well as the difference between convective and radiant heat transfer. This is why accurate cooling design calculations require the use of sophicated software like DesignBuilder and cannot simply be done in a spreadsheet by summing loads.

To help understand this more clearly, consider the extreme case of a building with very high thermal mass situated in a temperate climate. In this case there may be zero cooling requirement, even with significant internal solar and internal gains. So the cooling load is clearly not simply the sum of internal gains. Other less extreme cases can be considered in a similar way.