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AS3600 longitudinal shear
- Thread starter apsix
- Start date
Make sure you have the amendment for this because the equations given in 2009 didn't quite make sense.
I think the β/z term is introduced to replace the Q/I of elastic theory. Where for a rectangular section the greatest longitudinal shear occurs at the N.A and is equal to V*/(0.66*b*d). For a r.c section, the beta term takes the ratio of the internal coupling force at the location of the plane to the total coupling force (equal to 1.0 at the NA) and z being the coupling distance.
Say for a r.c section where the shear plane is at the neutral axis and ku is approximtaley 0.15. Then the longitudinal shear force will be 1.0*V*/(0.925*d*bf). Compare this to an elastic material where the longitindal shear stress is V*/(0.66*b*d).
I think the β/z term is introduced to replace the Q/I of elastic theory. Where for a rectangular section the greatest longitudinal shear occurs at the N.A and is equal to V*/(0.66*b*d). For a r.c section, the beta term takes the ratio of the internal coupling force at the location of the plane to the total coupling force (equal to 1.0 at the NA) and z being the coupling distance.
Say for a r.c section where the shear plane is at the neutral axis and ku is approximtaley 0.15. Then the longitudinal shear force will be 1.0*V*/(0.925*d*bf). Compare this to an elastic material where the longitindal shear stress is V*/(0.66*b*d).
The amendment Asixth is talking about is to equation 8.4.3. The bf term should be ommitted.
The two terms you have questioned are defined in 8.4.2. I am not sure how to add to the definitions.
z is the lever arm for ultimate strength, so the distance between the centroids of the tension and compression forces.
beta is defined separately depending on the depth at which you are doing the calculations.
if the depth is within the compression zone, it is the ratio of the amount of compression force in the zone above the depth you are investigating to the total compression force at the cross-section.
The only hassle I see in this calculation is use of the rectangular stress block (which I do not use) and how to estimate how much of the compression force in the rectangular stress block is above the point considered when you consider the logic of a rectangulat stress block and how it was developed. It is not logical! Assuming the concrete force depth is actually the depth of the rectangular stress block rather than the neutral axis would be conservative as Beta would be higher than using a real stress strain curve so it is conservative!
The two terms you have questioned are defined in 8.4.2. I am not sure how to add to the definitions.
z is the lever arm for ultimate strength, so the distance between the centroids of the tension and compression forces.
beta is defined separately depending on the depth at which you are doing the calculations.
if the depth is within the compression zone, it is the ratio of the amount of compression force in the zone above the depth you are investigating to the total compression force at the cross-section.
The only hassle I see in this calculation is use of the rectangular stress block (which I do not use) and how to estimate how much of the compression force in the rectangular stress block is above the point considered when you consider the logic of a rectangulat stress block and how it was developed. It is not logical! Assuming the concrete force depth is actually the depth of the rectangular stress block rather than the neutral axis would be conservative as Beta would be higher than using a real stress strain curve so it is conservative!
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