This Blog post has some relations with the earlier post. I advise to read that post first.
Different elements in the bridge design
In the design some steps have to be prescribed. This is not about how a model works but how I think it should be build. It is done in this way because the equations are very large and so mistakes are made very soon.
In this prescription only a simple rectangular beam is used but also other shapes would be possible. This would only mean that different I-values are needed.
1) A certain area / floor plan is made. This floor plan has a load.
2) One central line, the basic line of the primary beam, is created out of the lines that create the area.
3) Some points on the central line are made. First they are used in making the basic line for secondary beams. Also they got used for the calculation of moments in this point.
The next steps can be done independently because they both only depend on the load.
A) The primary beam get its shape from a maximum committed tension. (earlier mentioned)
B) The secondary beam get its shape from maximum committed tension.
In both situations first the line of moments has to be found. This is easy in phase B but not so easy in phase A.
After that with maximum stress the cross sections of a beam can be calculated. This can only been done if decisions about the height and width relations are made.
A) The shaping of the primary beam
The primary beam is the support for the secondary beams. In this they all create a point load on the primary beam. Because the length of the secondary beam can change, also the point load on the primary beam can change.
Because the loads are known and the distances between the secondary beams can be calculated also the support points for the primary beam can be calculated. Then also the moments on every point on the basic line, where the support for the secondary beams take place, can be calculated.
From the moments in combination with the maximum tension and information about the width and the height relation the cross section on a certain point can be shaped. When these cross sections got connected the beam gets it shape.
In This picture the next values are showed:
y…. = length of the secondary beam
Fn = First support point of the primary beam
Fn+1 = Second support point of the primary beam
x…. = distance between secondary beams
The next equations the different values that are calculated:
By using these equations no cross section would exist in the support points of the primary beam. Of course this is not possible. A solution for this has to be found. A minimum cross section on this point has to be calculated. This can be done by introducing a maximum shear force that comes forward out of the support points in Point a and b.
B) The shaping of the secondary beam
From the points on the primary beam and the area / floor plan the basic lines for the secondary beams are created. The beam that is related to this line is thought of being fixed to the secondary beam. (for now the torsion that this creates is not used in the calculations but this will be important in shaping the construction and so it might be needed to use more beams than only one or to make other decisions)
As was told in the shaping of the primary beam also the secondary beam gets it shape from the maximum committed tension in the material. This is also done by using the line of moments and some information about the cross section height and width relations.
This construction is made with two different width and height relations in the cross section. In the first the relation gives that the width is half the height. In the second a constant width is given.
Different elements in the bridge design
In the design some steps have to be prescribed. This is not about how a model works but how I think it should be build. It is done in this way because the equations are very large and so mistakes are made very soon.
In this prescription only a simple rectangular beam is used but also other shapes would be possible. This would only mean that different I-values are needed.
1) A certain area / floor plan is made. This floor plan has a load.
2) One central line, the basic line of the primary beam, is created out of the lines that create the area.
3) Some points on the central line are made. First they are used in making the basic line for secondary beams. Also they got used for the calculation of moments in this point.
The next steps can be done independently because they both only depend on the load.
A) The primary beam get its shape from a maximum committed tension. (earlier mentioned)
B) The secondary beam get its shape from maximum committed tension.
In both situations first the line of moments has to be found. This is easy in phase B but not so easy in phase A.
After that with maximum stress the cross sections of a beam can be calculated. This can only been done if decisions about the height and width relations are made.
A) The shaping of the primary beam
The primary beam is the support for the secondary beams. In this they all create a point load on the primary beam. Because the length of the secondary beam can change, also the point load on the primary beam can change.
Because the loads are known and the distances between the secondary beams can be calculated also the support points for the primary beam can be calculated. Then also the moments on every point on the basic line, where the support for the secondary beams take place, can be calculated.
From the moments in combination with the maximum tension and information about the width and the height relation the cross section on a certain point can be shaped. When these cross sections got connected the beam gets it shape.
In This picture the next values are showed:
y…. = length of the secondary beam
Fn = First support point of the primary beam
Fn+1 = Second support point of the primary beam
x…. = distance between secondary beams
The next equations the different values that are calculated:
By using these equations no cross section would exist in the support points of the primary beam. Of course this is not possible. A solution for this has to be found. A minimum cross section on this point has to be calculated. This can be done by introducing a maximum shear force that comes forward out of the support points in Point a and b.
B) The shaping of the secondary beam
From the points on the primary beam and the area / floor plan the basic lines for the secondary beams are created. The beam that is related to this line is thought of being fixed to the secondary beam. (for now the torsion that this creates is not used in the calculations but this will be important in shaping the construction and so it might be needed to use more beams than only one or to make other decisions)
As was told in the shaping of the primary beam also the secondary beam gets it shape from the maximum committed tension in the material. This is also done by using the line of moments and some information about the cross section height and width relations.
This construction is made with two different width and height relations in the cross section. In the first the relation gives that the width is half the height. In the second a constant width is given.
The same pictures are possible for a simply supported beam with an equally divided load. This gives the next view.(is inserted in this blog in a later phase)
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