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]

I'll bite... and risk being humbled.

In all cases, the distance between one location of zero shear and the next gving, for your examples, maximums of:

1) L/2
2) L
3) 5L/8 (span = 2L)

Shear span is generally referenced in examining the angle of possible concrete struts assuming load resistance via arching action with each shear span representing a single half arch.

The definition of shear span and, in particular, the M/V version, is only strictly applicable to cases where all loads are concentrated.

 

[StructuralAddict]

Thanks KootK.. That was really helpful.
The Shear Span to depth ratio (M/Vdv) is used in the design of Masonry beams.
From what I know is that the shear span (M/V) is the length where shear is constant. So, it was confusing for me on how to calculate (M/V) for uniformly loaded beam when designing Masonry beams.

 

[KootK]

In that context, I believe that M/Vdv is the value based on the moment and shear present at the cross section being studied.

 

[BAretired]

Shear span is usually defined as the portion of a beam where shear is constant. That being the case the answers are:
1) 0 (there is no shear span)
2) L
3) 0 (there is no shear span)

If there is some other definition for shear span when designing masonry beams, perhaps a different name should be found.

BA

 

[StructuralAddict]

I believe the definition of shear span is confusing. I don't understand how the shear span is zero in a uniformly loaded simple beam. (By definition, shear span is length where shear is constant)..

 

[r13]

What is the shear when a beam loaded with a concentrated load only. Also, a cantilever with a concentrated load at any location along the beam.

 

[phamENG]

StructuralAddict - in a uniformly loaded beam, the shear varies linearly from a positive max on one end, to zero at midspan, to a negative max at the other end. Decidedly not constant along it's length. Hence the shear span of 0 for that case.

 

[RPMG]

Shear span doesn't exist. M/V is an expression.

 

[r13]

An example response from the web:

Shear span is the distance from the point of application of concentrated force to its respective Reaction force (supporting column).
Throughout single Shear Span the Shear Force is constant, i.e. have same value of Shear Force throughout a single Shear Span. There might be multiple (varying) shear span for a single Beam depending upon number & position of applied force to the numbers of supports.

Here, you can see a1 and a2 are the two different shear span for the same beam.

 

[r13]

Example of shear span = 0:

Shear span is defined as the zone where shear force is constant.
Reference : “What is shear span?”
Typical bending moment and shear force diagram of uniformly loaded is beam is given below.

Since, shear force is not constant between any span within the beam. So, shear span is 0.

 

[RPMG]

Very academic.

Does Not Exist.

 

[r13]

RPMG,

Sort of. It was used in studies of concrete beam shear behaviors in the past/ancient time

 

[StructuralAddict]

So, this means in masonry beam design, we calculate actual [M/(V.dv)] at the section we are designing the beam at (as KootK mentioned previously in this post). We do not substitute M/V = 0 (where the term M/V is called Shear Span).

 

[r13]

BAretired has the correct answers.

 

[KootK]

So, this means in masonry beam design, we calculate actual [M/(V.dv)] at the section we are designing the beam at (as KootK mentioned previously in this post). We do not substitute M/V = 0 (where the term M/V is called Shear Span).

Yesir. It's not as though the shear span has no physical meaning in this context. As shown below:

1) The shear capacity depends on the nature of the shear failure.

2) The nature of the shear failure depends on the angle of the principle tensions stress.

3) The angle of the principle tension stress depends on how much flexure is present in conjunction with the shear.

4) In order to be able to say whether or not a moment is "large" in this context, we need a parameter of a similar dimension with which to compare it. For that purpose, we use the moment that the shear force would produce acting over an eccentricity equal to dv (M = V x dv).

In this sense, M/Vdv is used as an index or something like a unit-less measure of moment "bigness" relative to the shear.

 

[BAretired]

So, this means in masonry beam design, we calculate actual [M/V.dv)] at the section we are designing the beam at (as KootK mentioned previously in this post). We do not substitute M/V = 0 (where the term M/V is called Shear Span).

I don't know what you mean by M/V.dv. What is dv?

No one is suggesting that M/V = 0. For a simple beam with uniform load w, M = wx(l-x)/2 where x is the distance from the left support. There is no shear span because there is no portion of the span where shear is constant.

A beam loaded with two point loads 'P' each applied at 'a' from each end has a shear span of 'a', a reaction of P, a moment varying linearly from reaction to load point and a constant moment P*a between the applied loads.

You seem to be re-inventing the term "shear span". It is not defined as M/V or M/V.dv, whatever that means.


BA

 

[StructuralAddict]

BAretired: The allowable shear stress due to masonry is given as:
Fvm = 0.5[4.0-1.75(M/(V.dv))].sqrt(f'm)+0.25(P/An)
Where:
M/V is the shear span
dv is the section depth considered in calculating shear force (Web depth)

 

[StructuralAddict]

Thanks KootK for your great explanation..

 

[BAretired]

StructuralAddict, I'm not familiar with the expression you cited for Fvm. You do not provide a source, but I assume it came from some building code. I am neither confirming nor disputing the formula; I am addressing the term "shear span" which you used in the OP without any reference to masonry.

For a uniform load on a simple beam, M[sub]x[/sub] = wx(l-x)/2 and V[sub]x[/sub] = w(l/2-x).
So M[sub]x[/sub]/V[sub]x[/sub] = x(l-x)/(l-2x). Mx/Vx varies throughout the span, approaching infinity at midspan. Call it M/V if you wish, but it is certainly not the shear span.

BA