Limit state design of beams is the type oof beam design perspective where by a beam is designed in such a way that it cannot fail to its intended purpose. The beam is designed in some of limit conditions so that it cannot fail. Here there are factors considered for safety.
For example, in order to limit maximum dead loads we multiply the dead load by 1.4, as well as in live loads we tend to multiply by 1.6.
Limit state design of beams is based on the following ways.
1. Load determination.
This is the first thing to consider once you are designing a beam under limit state design. Where a designer needs to determine types of loads that will appear on his building and, he or she will design a beam basing on such loads. Consider the types of loads below that mostly appear on buildings.
i. Dead loads - the type of loads that is due permanent structures on the building for example the building itself as well as fermetures that will be fixed on the building like cupboards.
ii. Live loads - the type of load that is kindly due to temporary appearing loads on the building and most of these loads are not constant, may vary for sometimes. For example, people living in a room or students in certain class may not be constant in that room.
iii. Wind loads – the type of loads due to horizontal air forces facing a particular building. For example, sea breeze facing the coastal buildings.
Therefore, in beam designing under limit state design you should determine the total loads on the structure by using the following formula, but this is on based to BS 8110.
Total loads = (dead loads x factor of safety) + (live load x factor of safety) + (wind load x factor of safety).
Total loads = (dead loads x 1.4) + (live loads x 1.6) + (wind loads x 1.4).
2. Bending moment determination.
Since most of beam are facing uniformly distribute loads, therefore bending determination is that of uniformly distributed loads. It is difficult to meet with a beam designed directly straight for point loads overcoming. Therefore, the bending moment is determined by the following formula, Note the formular is just because of uniformly loads.
Bending moment = wl2/4.
Where by “W” represents total design loads typically determined in first procedure with consideration of partial of safety. Also “L” is the effective length of the beam.
Note the values of “L” are found by; clear distance on the beam + half of width supports on both sides, or clear distance + effective span on the beam.
Consider the picture below
3, checking the values of “K” if is within the range or not.
The value of “K” ranges from 0.043 to 0.156, if the value is smaller than the minimum accepted value, you need to use the minimum one. Also, if the values are greater than the maximum allowable you have to design a doubly reinforced beam.
The values of K is found by the following formula;
K=M/bd2fcu
Use minimum value of “K” if K< 0.043, design doubly reinforced beam if K > 0.156
4. Determining the area of steel.
The values of K obtained in above step is useful in finding the area of steel required in a particular section. The are of steel using the following formula;
(area of steel for singly reinforced beam)
Area of steel = M/0.86fyz.
After getting the values of area of steel you need now to determine whether the values are within the limit or not.
Therefore these are the prior stages to design a beam especially for simply supported beam
