Why eurocode provide two equations? what is the use case in this?

[Pretty Girl7]

I'm calculating shear r/f,

So, I came across with the following two equations for concrete beam shear reinforcement, mentioned at totally different pages in the same Eurocode2.

I already calculated the Cot theta angle (strut angle). And I can see that can feed the "design shear (Ved)" directly into the second equation and get the required "reinforcement/space" ratio.

But, what is the use case of the first equation? When should I use it? Why there are two equations?

 

[bkal]

The second of your two equations calculates shear resistance (capacity) of your section and should be used to demonstrate that the section has sufficient capacity to withstand the applied load. The first equation is just an expression to calculate shear reinforcement ratio, i.e. relative area of shear reinforcement (to gross section) and should be used to confirm that provided shear reinforcement is greater than required minimum (which is provided by equation 9.5).

 

[HTURKAK]

- The clause 9.2.2.5 and the Expression (9.4) gives the ratio of shear reinforcement ..

- You can Calculate area of shear reinforcement with second expression ..








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[Pretty Girl7]

The second of your two equations calculates shear resistance (capacity) of your section and should be used to demonstrate that the section has sufficient capacity to withstand the applied load. The first equation is just an expression to calculate shear reinforcement ratio, i.e. relative area of shear reinforcement (to gross section) and should be used to confirm that provided shear reinforcement is greater than required minimum (which is provided by equation 9.5).

Thank you for the information.

Both provides shear r/f ratio if you re-arrange them. You can isolate "Asw/s" for both the equations.

Since the second equation to calculate shear resistance Why Can't I use the same equation to calculate the required shear r/f? If I apply the "Design shear force" to "Vrd,s" it outputs required r/f to resist the "design shear force". Am I wrong?.

How come second equation is inaccurate to calculate required shear r/f than the first equation?

As I see, the second equation can do both section strength check and then calculate the required shear. Why I shouldn't only use the second equation?

 

[Pretty Girl7]

- The clause 9.2.2.5 and the Expression (9.4) gives the ratio of shear reinforcement ..

- You can Calculate area of shear reinforcement with second expression ..

Thank you for the information.

If you re-arrange and isolate "Asw/s", both the equations provides the ratio of reinforcement, won't they? So, why can't I just use the first equation only to get the required shear r/f? I still don't get the unique use of having two equations.

 

[ThomasH]

@Pretty Girl7

You have now asked a lot of questions about the Eurocode. But I think you often miss a important factor regarding how to use the Eurocode, the Eurocode is often about context. Similar "equations" can have different purposes depending on the context.

If you take EC 2, 6.2.3 it describes "Members requiring design shear reinforcement". Section 6 is Ultimate Limit States (ULS) and the first sentence in 6.2.3 mentions "Shear reinforcement is based on a truss model". There are other shear models available but in this context it's a truss model for the shear.

If you instead refere to Section 9 the title is "Detailing of members and particular rules". The equation you have there describes the shear reinforcement ratio. And the context is that there is a minimum required amount of reinforcement in the beam. Otherwise, the beam is not considered as having shear reinforcement.