Effective span example 2

In this section we will calculate the effective spans of the continuous beam shown in the fig.7b.1 below:

Fig.7b.1
Plan and elevation of continuous beam

From the fig., we can see that, in this problem, the supports have different widths. The outer most supports have a width of 300mm, the inner supports have a width of 230 mm, and the inner most support have a width of 200mm. 

We will calculate the effective spans by the two different methods: The one based on Eurocode-2, and the other based on IS 456. For this problem, it is convenient to mention before hand that, each of the spans have their support widths less than it's ln/12. So while using the cl.22.2(b) of IS 456, we will not have to look to the portion below the magenta colored dashed line of the chart.

Also assume dia. of bottom bars = 20 mm and dia. of links = 8 mm

So effective depth d = 450 -30 -8 -10 = 402 mm

First we will consider span AB. The calculations based on Eurocode-2 (fig) is shown in Table 7b.1 below:

Table 7b.1
Span AB, l_n =4300

	Support A	Support B
Type of support	Non-continuous support	Continuous support
Fig. to use	Fig.(a)	Fig.(b)
h	450	450
t	300	230
ai = lesser of {h/2; t/2}	150	115

l_eff = l_n + a₁ +a₂ =4300 +150 +115 =4565

The calculations based on IS 456 is given below:
Clear span l_n =4300mm.
l_n/12 = 4300/12 =358.33. So t₁ < l_n/12 & t₂ < l_n/12

As mentioned above, we only need the portion above the magenta colored dashed line for all spans of the beam. This is shown in the fig.7b.2 below. This fig. is applicable to all the spans.

Fig.7b.2
Application of chart to span AB

Now we calculate the following:
• c/c distance between the supports = 4300 +150 +115 =4565
• clear span + effective depth = 4300 +402 =4702
Effective span = l_eff = Lesser of the above = 4565mm

Thus we calculated l_eff of span AB using the two methods.

Now we will consider span BC. The calculations based on Eurocode-2 is shown in Table 7b.2 below:

Table 7b.2
Span BC, l_n =4000

	Support B	Support C
Type of support	Continuous support	Continuous support
Fig. to use	Fig.(b)	Fig.(b)
h	450	450
t	230	200
ai = lesser of {h/2; t/2}	115	100

l_eff = l_n + a₁ +a₂ =4000 +115 +100 =4215

The calculations based on IS 456 is given below:
Clear span l_n =4000mm.
l_n/12 = 4000/12 =333.33. So t₁ < l_n/12 & t₂ < l_n/12

Fig.7b.2 is applicable here also. Now we calculate the following:
• c/c distance between the supports = 4000 +115 +100 =4215
• clear span + effective depth = 4000 +402 =4402
Effective span = l_eff = Lesser of the above = 4215mm

Thus we calculated l_eff of span BC using the two methods.

Now we will consider span CD. The calculations based on Eurocode-2 is shown in Table 7b.3 below:

Table 7b.3
Span CD, l_n =4365

	Support C	Support D
Type of support	Continuous support	Continuous support
Fig. to use	Fig.(b)	Fig.(b)
h	450	450
t	200	230
ai = lesser of {h/2; t/2}	100	115

l_eff = l_n + a₁ +a₂ =4365 +100 +115 =4580

The calculations based on IS 456 is given below:
Clear span l_n =4000mm.
l_n/12 = 4365/12 =363.75. So t₁ < l_n/12 & t₂ < l_n/12

Fig.7b.2 is applicable here also. Now we calculate the following:
• c/c distance between the supports = 4365 +100 +115 =4580
• clear span + effective depth = 4365 +402 =4767
Effective span = l_eff = Lesser of the above = 4580mm

Thus we calculated l_eff of span CD using the two methods.

Now we will consider span DE. The calculations based on Eurocode-2 is shown in Table 7b.4 below:

Table 7b.4
Span DE, l_n =4250

	Support D	Support E
Type of support	Continuous support	Non-Continuous support
Fig. to use	Fig.(b)	Fig.(a)
h	450	450
t	230	300
ai = lesser of {h/2; t/2}	115	150

l_eff = l_n + a₁ +a₂ =4250 +115 +150 =4515

The calculations based on IS 456 is given below:
Clear span l_n =4000mm.
l_n/12 = 4250/12 =354.17. So t₁ < l_n/12 & t₂ < l_n/12

Fig.7b.2 is applicable here also. Now we calculate the following:
• c/c distance between the supports = 4250 +115 +150 =4515
• clear span + effective depth = 4250 +402 =4652
Effective span = l_eff = Lesser of the above = 4515mm

Thus we calculated l_eff of span DE using the two methods. All the results from the two methods are tabulated below:

Table 7b.5: Effective spans

Name of span	Based on Euro code	Based on IS456
AB	4565	4565
BC	4215	4215
CD	4580	4580
DE	4515	4515

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.





                                                         

            Copyright©2015 limitstatelessons.blogspot.in - All Rights Reserved