Calculating Maximum Moments of Cantilever Structures

Cantilever is the most daring of all the structures being built. The beauty of a legless front entrance canopy or shed is really stunning. However, wrong calculation of the maximum design moment of the structure may lead to structural failure when ultimate loading condition is reached.

Cantilever shed failed during 4.6 magnitude earthquake. Age might be one of the factors.

For basic cantilevers, earthquake is the main lateral (horizontal) load to be considered in addition to the vertical dead and live loads. Wind might prevail if the structure is too high and the columns are covered with wind resisting panels.

Considering dead load, live load and earthquake loads, here are the load combinations that we need to consider based on NSCP 2010.

1. U = 1.2D +1.6L
2. U = 1.2D + E + 0.5L

I eliminated other combinations which will obviously yield lower result.

From the load diagram below, we can calculate the maximum base moment based on the given equations.

By taking summation of moments at point A...

Mu = X^2/2(1.2D + 1.6L)                -> Equation 1
Mu = X^2/2(1.2D + 0.5L) + EH      -> Equation 2

We just need to substitute actual values here to see which equation would yield a greater result. Whichever resulting value is greater, that would be the design moment that should be used.

Example:

Given:
            D = 15kN/m
            L = 6 kN/m
            E = 3kN
            H = 4m
            x = 2m


Solution:
Equation 1     Mu = X^2/2(1.2D + 1.6L)
                             = 2^2/2(1.2*15 + 1.6*6)
                             = 64.2 kNm

Equation 2     Mu = X^2/2(1.2D + 0.5L) + EH
                             = 2^2/2(1.2*15 + 0.5*6) + 3*4
                             = 63 kN

Since Equation 1 yielded greater result, therefore Mu = 64.2 kNm

Assuming we will use a 300 mm x 300 mm concrete column, by applying reinforced concrete design formulas, use:

300 x 300 concrete column with 12-Ø20 RSB.