Shear strength of Round Section

[KarlT]

How would everyone calculate the effective shear area of a concrete beam with a circular cross section?

Normally, with a rectangular section the shear resistance is a function of bw*d.

However, with a round section bw is harder to figure out. For now I am assuming an equivalent square section, with an effective bw=0.8*Diameter , and with the top of the equivalent rectangular section at the top of the circular section. Then I am assuming that d = 0.8*Diameter as well.

Is this right?

 

[SlideRuleEra]

Your assumptions should be fine. Area of the square crossection = Area of the circular crossection.

 

[Taro]

That is essentially what the AISC HSS spec says. They give the nominal shear strength of a round section (meeting slenderness limits) as 0.3*Fy*Ag. This gives the same result as 0.6*Fy*Aw for a square tube with the same area.

 

[KarlT]

Actually the reason I'm asking the question is to try and calculate the shear strength of a round hollowcore void when it is filled with concrete. When the shear strength of a precast hollowcore floor slab is exceeded (either by adding an opening and removing webs or by heavily loading a member) you can gain additional shear strength by filling the remaining voids with concrete, while the hollowcore is still in a plastic state (right after extrusion). So in this case I am actually wondering what to use for "d" since there is no steel added in the void in this case.

 

[Qshake]

For round sections AASHTO states,

D need not be less than the distance from the extreme compression fiber to the centroid of the longitudinal tension reinforcement.

 

[Taro]

Sorry, I didn't read the question carefully enough and thought you were asking about steel sections.

For shear of circular concrete members, ACI 11.3.3 says "the area used to compute Vc shall be taken as the product of the diameter and effective depth of the concrete section. It shall be permitted to take the effective depth as 0.8 times the diameter of the concrete section."

The commentary says "Shear tests of members with circular sections indicate that the effective area can be taken as the gross area of the section or as an equivalent rectangular area."