Minimum Thickness of Concrete Beams and Slabs

One of the common mistakes being committed by some builders, who rely on experience and not on structural calculations, is not observing the minimum thickness or depth of concrete beams and slabs specified in the code.

The code specified minimum thicknesses for different types of support in order to prevent excessive deflection or sagging on site.

NSCP 2010 states the following...

...where L is the length of beam or one way slab and the denominator is the dividing factor. Length in beams is obvious. It is simply the center to center distance of the columns that support the beam. In one way slabs, however, the design length is not the longer side of the slab. It is wiser to design one way slabs considering the shorter side. For example, if you have a 2m x 4m slab, we take the 2m as the length of the slab and design it as a 1m-wide strip beam.

Example: Calculate the minimum thickness of 6m long beam with both ends continuous.

Given:

     Type of Structure:    Beam
     Type of Support:      Both ends continuous
     Length of beam:      6m

Solution:

     Based on the table, the minimum thickness for a beam with both ends continuous is L/21.

Therefore:

     T = L/21
        = 6m / 21
        = 0.286 m or 286 mm

Here is the program that automatically calculates minimum thickness of concrete beams and slabs:
Click here and download the file -> Concrete Beam and Slab Thickness Calculator

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.

1.4DL + 1.7LL or 1.2DL + 1.6LL ?

For designers like me who were trapped in the past (used to using the old codes), the introduction of new and smaller load factors might be quite hard to accept. In school, we were taught to use 1.4DL + 1.7LL in calculating the ultimate load involving basic dead and live loads. However in the latest NSCP which was released a few years ago, the new load factors are smaller - 1.2DL + 1.6LL.

Below is the table showing the comparison of the new and old codes:

Where:

D = dead load

E = earthquake load 

F = load due to fluids

H = load due to lateral pressure of soil and water in soil

L = live load, except roof live load, including any permitted live load reduction

Lr = roof live load , including any permitted live load reduction

R = rain load on the undef1ected roof

T = self-straining force and effects arising from contraction or expansion resulting from temperature change, shrinkage, moisture change, creep in component materials, movement due to differential settlement, or combinations thereof .

W = load due to wind  pressure

f1 = 1.0 for floors in places of public assembly, for live loads in excess of 4.8 kPa, and for garage live load.

= 0.5 for other live loads

Em = the maximum effect of horizontal and vertical forces as set forth in Section 208.6.1

Which one should we use? In practice, we could use any of these based on engineers discretion because presumably, both of them are safe to apply and there has been lots of studies, researches and experimentation done before structural scientists came up with the numbers. In schools, however, I am not sure if they are using the new code. If the professor says use the new code then use the new code otherwise you'll get the wrong answer because of using the load factors in the old code.

Standard Hooks and Minimum Bends

According to NSCP, for a certain bar size, there is a standard minimum size of bend and length of extension.

Here is the easy tabular and graphical interpretation of the code regarding bends and hooks.

The table below shows the numerical values of the table above.