In this section we will calculate the effective spans of the continuous slab shown in the fig.7d.1 below:
Fig.7d.1
Plan and elevation of continuous beam
From the fig., we can see that, in this problem, all the supports have equal width. We will calculate the effective spans by the two different methods: The one based on Eurocode-2, and the other based on IS 456.
Assume dia. of bottom bars = 10 mm, and Cc =30mm. So effective depth d = 150 -30 -5 = 115 mm
First we will consider span AB. The calculations based on Eurocode-2 is shown in Table 7d.1 below:
Table 7d.1
Span AB, ln =2850
Clear span ln =3500mm.
ln/12 = 2850/12 =237.5. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {237.50 ; 600}, which is 237.50. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
Thus we take the deviation to the right. The path taken by the calculations is shown in the fig.7d.1 below:
Fig.7d.1
Application of chart to span AB
At 'A', the deviation is towards the right. If at 'A', the deviation is to the right, we will be needing the whole portion of the chart. So proceeding downwards, at 'B', the deviation is towards the left because, the span AB that we are considering, is an End span. Next, at 'C', the deviation is towards the right because, span AB has one end free, and the other end continuous. Thus we reach a 'blue box' which gives us the steps in the final calculations that have to be made.
So we calculate the following:
• clear span + 0.5 x effective depth =2850 + 0.5 x115 =2907.5
• clear span + 0.5 x width of discontinuous support =2850 + 0.5 x300 =3000
Effective span = leff = Lesser of the above = 2907.5mm
Thus we calculated leff of span AB using the two methods.
Now we will consider span BC. The calculations based on Eurocode-2 is shown in Table 7d.2 below:
Table 7d.2
Span BC, ln =3300
Clear span ln =3300mm.
ln/12 = 3300/12 =275.00. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {275.00 ; 600}, which is 275.00. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
Thus we take the deviation to the right. The path taken by the calculations is shown in the fig.7d.2 below:
Fig.7d.2
Application of the chart to span BC
The path taken is different from that in the previous fig.7d.1. This is because the previous span AB is an end span. The present span BC is an intermediate span. So here, the deviation at 'B' is towards the right. After this point, there is no other deviations, and we reach a 'blue box'. Thus the effective span is the clear span between the supports. So we can write:
leff of span BC = 3300
Thus we calculated leff of span BC using the two methods.
Now we will consider span CD. The calculations based on Eurocode-2 is shown in Table 7d.3 below:
Table 7d.3
Span CD, ln =3450
Clear span ln =3300mm.
ln/12 = 3300/12 =275. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {275 ; 600}, which is 275. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
The fig.7d.2 is applicable here also because CD is also an intermediate span just like BC. Thus the effective span is the clear span between the supports. So we can write:
leff of span CD = 3300
Thus we calculated leff of span CD using the two methods.
Now we will consider span DE. The calculations based on Eurocode-2 is shown in Table 7d.4 below:
Table 7d.4
Span DE, ln =2850
Clear span ln =2850mm.
ln/12 = 2850/12 =237.50. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {237.5 ; 600}, which is 237.5. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
The first fig.7d.1 is applicable here also because DE is also an end span just like AB
So we calculate the following:
• clear span + 0.5 x effective depth =2850 + 0.5 x115 =2907.5
• clear span + 0.5 x width of discontinuous support =2850 + 0.5 x300 =3000
Effective span = leff = Lesser of the above = 2907.5mm
Thus we calculated leff of span DE using the two methods. All the results from the two methods are tabulated below:
We have branched off from the main discussion. The layout map given below will help us to navigate easily between the various sections. Links to some more examples are also given in the layout map.
Fig.7d.1
Plan and elevation of continuous beam
From the fig., we can see that, in this problem, all the supports have equal width. We will calculate the effective spans by the two different methods: The one based on Eurocode-2, and the other based on IS 456.
Assume dia. of bottom bars = 10 mm, and Cc =30mm. So effective depth d = 150 -30 -5 = 115 mm
First we will consider span AB. The calculations based on Eurocode-2 is shown in Table 7d.1 below:
Table 7d.1
Span AB, ln =2850
| Support A | Support B | |
| Type of support | Non-continuous support | Continuous support |
| Fig. to use | Fig.(a) | Fig.(b) |
| h | 150 | 150 |
| t | 300 | 300 |
| ai = lesser of {h/2; t/2} | 75 | 75 |
leff = ln + a1 +a2 =2850 +75 +75 =3000
The calculations based on IS 456 is given below:Clear span ln =3500mm.
ln/12 = 2850/12 =237.5. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {237.50 ; 600}, which is 237.50. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
Thus we take the deviation to the right. The path taken by the calculations is shown in the fig.7d.1 below:
Fig.7d.1
Application of chart to span AB
At 'A', the deviation is towards the right. If at 'A', the deviation is to the right, we will be needing the whole portion of the chart. So proceeding downwards, at 'B', the deviation is towards the left because, the span AB that we are considering, is an End span. Next, at 'C', the deviation is towards the right because, span AB has one end free, and the other end continuous. Thus we reach a 'blue box' which gives us the steps in the final calculations that have to be made.
So we calculate the following:
• clear span + 0.5 x effective depth =2850 + 0.5 x115 =2907.5
• clear span + 0.5 x width of discontinuous support =2850 + 0.5 x300 =3000
Effective span = leff = Lesser of the above = 2907.5mm
Thus we calculated leff of span AB using the two methods.
Now we will consider span BC. The calculations based on Eurocode-2 is shown in Table 7d.2 below:
Table 7d.2
Span BC, ln =3300
| Support B | Support C | |
| Type of support | Continuous support | Continuous support |
| Fig. to use | Fig.(b) | Fig.(b) |
| h | 150 | 150 |
| t | 300 | 300 |
| ai = lesser of {h/2; t/2} | 75 | 75 |
leff = ln + a1 +a2 =3300 +75 +75 =3450
The calculations based on IS 456 is given below:Clear span ln =3300mm.
ln/12 = 3300/12 =275.00. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {275.00 ; 600}, which is 275.00. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
Thus we take the deviation to the right. The path taken by the calculations is shown in the fig.7d.2 below:
Fig.7d.2
Application of the chart to span BC
The path taken is different from that in the previous fig.7d.1. This is because the previous span AB is an end span. The present span BC is an intermediate span. So here, the deviation at 'B' is towards the right. After this point, there is no other deviations, and we reach a 'blue box'. Thus the effective span is the clear span between the supports. So we can write:
leff of span BC = 3300
Thus we calculated leff of span BC using the two methods.
Now we will consider span CD. The calculations based on Eurocode-2 is shown in Table 7d.3 below:
Table 7d.3
Span CD, ln =3450
| Support C | Support D | |
| Type of support | Continuous support | Continuous support |
| Fig. to use | Fig.(b) | Fig.(b) |
| h | 150 | 150 |
| t | 300 | 300 |
| ai = lesser of {h/2; t/2} | 75 | 75 |
leff = ln + a1 +a2 =3300 +75 +75 =3450
The calculations based on IS 456 is given below:Clear span ln =3300mm.
ln/12 = 3300/12 =275. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {275 ; 600}, which is 275. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
The fig.7d.2 is applicable here also because CD is also an intermediate span just like BC. Thus the effective span is the clear span between the supports. So we can write:
leff of span CD = 3300
Thus we calculated leff of span CD using the two methods.
Now we will consider span DE. The calculations based on Eurocode-2 is shown in Table 7d.4 below:
Table 7d.4
Span DE, ln =2850
| Support D | Support E | |
| Type of support | Continuous support | Non-Continuous support |
| Fig. to use | Fig.(b) | Fig.(a) |
| h | 150 | 150 |
| t | 300 | 300 |
| ai = lesser of {h/2; t/2} | 75 | 75 |
leff = ln + a1 +a2 =2850 +75 +75 =3000
The calculations based on IS 456 is given below:Clear span ln =2850mm.
ln/12 = 2850/12 =237.50. So t1 ≮ ln/12 & t2 ≮ ln/12
Note the 'Not less than' symbol in the above step. So we cannot turn left. Let us see if we can turn right: For this, we have to calculate the lesser of {ln/12; 600} That is., the lesser of {237.5 ; 600}, which is 237.5. So we can write:
t1 > lesser of {ln/12 ; 600} & t2 > lesser of {ln/12 ; 600}
The first fig.7d.1 is applicable here also because DE is also an end span just like AB
So we calculate the following:
• clear span + 0.5 x effective depth =2850 + 0.5 x115 =2907.5
• clear span + 0.5 x width of discontinuous support =2850 + 0.5 x300 =3000
Effective span = leff = Lesser of the above = 2907.5mm
Thus we calculated leff of span DE using the two methods. All the results from the two methods are tabulated below:
Table 7d.5: Effective spans
| Name of span | Based on Euro code | Based on IS456 |
| AB | 3000 | 2907.5 |
| BC | 3450 | 3300 |
| CD | 3450 | 3300 |
| DE | 3000 | 2907.5 |
We have branched off from the main discussion. The layout map given below will help us to navigate easily between the various sections. Links to some more examples are also given in the layout map.
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