In
the previous section we completed the discussion on 'Analysis of Beam sections'. In the present section we will see the 'Design'. We
will first have a brief discussion about what is actually meant by
'Design': Consider a structural member like a beam, a slab or a
column., in a structure. The structure can be a large multi
storeyed framed structure, a single storeyed or two storeyed
residential building, or any other similar structure. A structural
member like a beam, will be acted upon by different types of loads.
These loads can be Dead loads, Live loads, Wind loads, Seismic loads
etc., These loads will cause various types of effects on the beam.
For example, some of the loads may try to bend the beam. In this case, we say that the beam is subjected to 'Bending moments'. 'Resisting moments' will develop in the beam, and this resisting moments should be greater than or equal to the external moment which tries to bend the beam. We can say that the flexural strength of the beam is being put to test.
Some of the loads may try to twist the beam. So the beam should have enough torsional strength. Some loads may cause shearing forces. So the beam should have enough shear strength. In addition, there may be shrinkage and temperature effects. Similarly, there are many types of loads and load effects. We will see them in subsequent chapters. The purpose of 'Design' is to make a structural member 'capable' to resist what ever loads and load effects it may be subjected to, during the life time of the structure.
But the design will be complete only when we make it capable to resist all the load effects on it. So in later chapters, we will see the design for shear, torsion etc.,
To calculate the self wt., we must know the cross sectional dimensions of the beam. But the exact cross sectional dimensions can be fixed only after the design, and doing the required design checks. So this forms a loop as shown in the fig.4.2 below:
Fig.4.2
Formation of loop in calculating Self weight
So we have to use a trial and error method. In this method, we fix up some preliminary dimensions for the member. Based on these dimensions, we calculate the self wt. Once we get the dimensions and self wt., we can do the structural analysis and get the BMD. From the BMD, we can obtain the maximum BM, and the position of the beam section where this maximum BM occurs. So we can design that beam section. If the preliminary dimensions are found to be inadequate, they must be discarded, and the process must be started again using improved dimensions.
So we want a method for fixing up preliminary dimensions of the beam. We can use some general rules that are followed traditionally by designers. One such rule to fix up a preliminary 'depth' of the beam, is:
4.1
to use Span to Overall depth ratios of 10 to 16. That is., l/D ratio is given a value in the range of 10 to 16. The value of D calculated from this ratio must be rounded off to the nearest multiple of 25 or 50mm. This is because, the side boards of formworks generally have heights which are multiples of 25 or 50mm
In this ratio, the Overall depth (Total depth) D is in the denominator. So as the span increases, D also increases. The range from 10 to 16 is found to be economical for simply supported and continuous beams. For cantilevers lower values are given to this ratio. So for cantilevers, greater D will be obtained from the ratio. Also cantilevers are generally tapered along their length, with the top surface horizontal and the depth decreasing as we move away from the support. In this case, the D that is calculated is given near the support.
In the next section, we will see the method to fix up a preliminary value for the width b of the section.
For example, some of the loads may try to bend the beam. In this case, we say that the beam is subjected to 'Bending moments'. 'Resisting moments' will develop in the beam, and this resisting moments should be greater than or equal to the external moment which tries to bend the beam. We can say that the flexural strength of the beam is being put to test.
Some of the loads may try to twist the beam. So the beam should have enough torsional strength. Some loads may cause shearing forces. So the beam should have enough shear strength. In addition, there may be shrinkage and temperature effects. Similarly, there are many types of loads and load effects. We will see them in subsequent chapters. The purpose of 'Design' is to make a structural member 'capable' to resist what ever loads and load effects it may be subjected to, during the life time of the structure.
So
how do we make it 'capable'? By giving the required dimensions, by
giving the required quantity and grade of steel reinforcements, by
giving the required grade of concrete, by giving the required
concrete cover to reinforcements etc.,, we will be making a
structural member, which is capable to resist all the loads that can
possibly act on it. So the first step is to obtain the load effects.
For
example: Consider the situation when we are asked to design a beam. We want more
information:
• We want to know whether the beam is subjected to bending?. If yes, what is the magnitude of the bending moment acting on it?
• We want to know if there are any shear forces acting on the beam. If yes, what are the magnitudes of the shear forces?
Similar is the case with torsion, and other such effects. So the designer has to ask a series of questions. The answers to these questions are obtained when we do the 'structural analysis' of the whole structure. This analysis is different from the 'analysis of beam sections' that we saw in the previous chapter.
• We want to know whether the beam is subjected to bending?. If yes, what is the magnitude of the bending moment acting on it?
• We want to know if there are any shear forces acting on the beam. If yes, what are the magnitudes of the shear forces?
Similar is the case with torsion, and other such effects. So the designer has to ask a series of questions. The answers to these questions are obtained when we do the 'structural analysis' of the whole structure. This analysis is different from the 'analysis of beam sections' that we saw in the previous chapter.
Several
methods are available to do the structural analysis. For example,
'Kani's method' can be used to obtain the Bending moments and shear
forces, caused by Vertical loads in a framed structure. 'Portal
method' or 'Cantilever method can be used to obtain the bending
moments and shear forces caused by lateral loads like wind loads and
seismic loads in a framed structure. Standard text books on
structural analysis should be referred to get a good understanding
about the application of these and similar other methods.
The
structural analysis can be completed in just two or three steps in
the case of some very simple structures. For example, consider a beam
of effective span 'l' which is simply supported on two walls, as shown below in fig.4.1.
Fig.4.1
Beam simply supported on walls
This beam is an isolated one, and is not connected to any other members like slabs, other beams, columns etc.,. If it is subjected to a characteristic UDL of w per meter length, and the characteristic self wt. is wDL per meter length, then the maximum BM M at midspan, and the Maximum shear force V at supports will be given by:
Fig.4.1
Beam simply supported on walls
This beam is an isolated one, and is not connected to any other members like slabs, other beams, columns etc.,. If it is subjected to a characteristic UDL of w per meter length, and the characteristic self wt. is wDL per meter length, then the maximum BM M at midspan, and the Maximum shear force V at supports will be given by:
It
must be noted that the above results are obtained from characteristic
loads. To obtain the factored BM and Shear force, factored loads must
be used.
So
now we know how to obtain the load effects. That is., we have the
additional information to start the design. In fact the designer will not have to ask the series of questions about the load effects. Whatever load effects are present, will be and should be written in the 'problem statement'.
In the design process, we make sure that:
In the design process, we make sure that:
• The
final completed design of the beam will be capable to resist the BM
obtained from the 'structural analysis'.
• The
final completed design of the beam will be capable to resist the
Shear force obtained from the 'structural analysis'.
• In
short the final completed design of the beam will be capable to
resist all the load effects obtained from the structural analysis. And also the effects such as shrinkage, creep, temperature effects etc.,
In
this chapter we will be discussing the design for flexure. That is.,
we will be making sure that the beam that we design will be capable
to resist the bending moments acting on it.
But the design will be complete only when we make it capable to resist all the load effects on it. So in later chapters, we will see the design for shear, torsion etc.,
Design of beam section for flexure:
We have seen that the 'Structural analysis' should be completed before taking up the design. From the results of the structural analysis, we can draw the 'Bending moment diagram' (BMD) of a beam. From the BMD, we can obtain the BM at any section of the beam. But for doing the Structural analysis, we must know the self wt. of the beam. Because self wt is also a component of the total DL acting on the beam. Also, for analysis of frames, the dimensions of the members are required to calculate the stiffness.To calculate the self wt., we must know the cross sectional dimensions of the beam. But the exact cross sectional dimensions can be fixed only after the design, and doing the required design checks. So this forms a loop as shown in the fig.4.2 below:
Fig.4.2
Formation of loop in calculating Self weight
So we have to use a trial and error method. In this method, we fix up some preliminary dimensions for the member. Based on these dimensions, we calculate the self wt. Once we get the dimensions and self wt., we can do the structural analysis and get the BMD. From the BMD, we can obtain the maximum BM, and the position of the beam section where this maximum BM occurs. So we can design that beam section. If the preliminary dimensions are found to be inadequate, they must be discarded, and the process must be started again using improved dimensions.
So we want a method for fixing up preliminary dimensions of the beam. We can use some general rules that are followed traditionally by designers. One such rule to fix up a preliminary 'depth' of the beam, is:
4.1
to use Span to Overall depth ratios of 10 to 16. That is., l/D ratio is given a value in the range of 10 to 16. The value of D calculated from this ratio must be rounded off to the nearest multiple of 25 or 50mm. This is because, the side boards of formworks generally have heights which are multiples of 25 or 50mm
In this ratio, the Overall depth (Total depth) D is in the denominator. So as the span increases, D also increases. The range from 10 to 16 is found to be economical for simply supported and continuous beams. For cantilevers lower values are given to this ratio. So for cantilevers, greater D will be obtained from the ratio. Also cantilevers are generally tapered along their length, with the top surface horizontal and the depth decreasing as we move away from the support. In this case, the D that is calculated is given near the support.
In the next section, we will see the method to fix up a preliminary value for the width b of the section.
Copyright ©2015 limitstatelessons.blogspot.com- All Rights Reserved
No comments:
Post a Comment