Shear Span 2

[StructuralAddict]

I appreciate if someone can give me an answer to this:
What is the shear span (M/V) of the following members?
1- uniformly loaded simply supported beam
2- cantilever with concentrated load at its tip
3- two-span continuous beam with uniformly distributed load on both spans

Thank you!

 

[KootK]

Sound about right?

Meh...I think that the most meaningful way to tell the story is to keep it focused on the shear span ratio serving as a measure of how much flexural stress one has acting on a cross section concurrently with the shear stress. It is that metric that locates a particular design section correctly on the continuum of shear failure modes and, therefore, shear capacity.

In this context, the use of the M/V shear span concept is nothing more than a way of describing the M/V ratio -- a particular way that would have reflected lab test setups. It's not until that ratio is divided by the shear depth that it becomes a suitable measure of the relative intensity of flexural stress.

Consider a little math where we are interested in an meaninngful index of the ratio of elastic flexural stress to shear stress rather than the actual value of it:

fb / fv = M/bd^2 / V/bd = M/Vd

That help at all?

 

[phamENG]

Makes sense to me. Well put. Many thanks.

 

[KootK]

Many welcomes. With respect to the termininology, it's akin to walking in on a MMF threesome (shear span ratio) and observing that it is a heterosexual couple (shear span) and a man (dv). It's not wrong; it's just a different way to describe it.

 

[r13]

In an effort to understand the physical implication of the shear span ratio, I did a parameter study on the cantilever column as shown below. Ignoring the contribution of the compressive stress (second term in the shear strength equation), the things I've noticed are: 1) The shear strength decreases when the column span to depth ratio increases (L/d). 2) The shear strength diminishes to zero once nearing the upper limit of deep beam classification mentioned previously - 2.5. 3) The theoretical maximum shear strength occurs when M = 0, then Fv = 2*sqrt(fm'), which is identical to shear strength of the reinforced concrete members (note this case is not associated with the cantilever under study).

After all, I still don't understand why M/Vd[sub]v[/sub] is set to 1.0, when larger ratio occurs. Any idea?

 

[r13]

[After thought]

From exercise above, the physical meaning of shear span ratio can be expressed as below:

- The shear stress resistance at the cantilever wall base is anticipated to be the minimum, when the wall height (L) to wall in-plan depth (d) is greater than 1. The allowable stress increases when the ratio is less than 1.
- The moment influences the masonry shear resistance in a negative way. Unlike the reinforced concrete, which allows the additional shear capacity for the presence of reinforcing steel, that provide better confinement - an effect similar to the term P/An.