Shear strength of concrete

[gkm111]

The shear strength of concrete (Canada) is given by the formula:
Vc = 0.2 x λ x ᶲc x √f'c x bw x d
Where λ = 1 for normal weight concrete
ᶲc = 0.6
f'c = compressive strength of concrete
bw = width
d = depth

Suppose we have a dowel (say rebar) in the center of a concrete panel with thickness 150mm.

If the dowel (15 mm) is placed at the centreline of the panel, then bw = 15 + 2 x 75 and d = 75

The question is, doesn't the length of the dowel have an effect on the shear strength? However there is nothing in the equation to account for the length? That is, doesn't the third dimension have an impact on the shear strength?

 

[KootK]

A sketch would help here. Is the "dowel" perpendicular to the applied shear or parallel to it? If the dowel is perpendicular to the applied shear, it will help with shear friction but not diagonal tension shear (the kind addressed by the equation that you quoted). Also, I'm not clear on why you've calculated bw as you have. I'm happy to help but more information is required.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[gkm111]

Sketch attached.

 

[KootK]

Ah... I see. Thanks for the sketch. Firstly, I'm not sure that one way shear is the way to go about this. I'd go with design provisions specific to dowel anchors, either the anchorage provisions of Canada's concrete code or perhaps something developed by the precast industry. The answer will be related to concrete shear, as all concrete breakout failure modes are, but likely formulated differently.

The length of the dowel will matter but only to a point. Beyond a certain distance, the flexibility of the dowel prevents it from engaging more concrete breakout surface. Back in the days before we had rigorous anchorage provisions, I was taught that six times the bar diameter was a good dowel length to consider effective.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Signious]

Hey, If you have it - crack open your A23.3 Book and flip to sect. 11.2.5

This References that shear reinforcement should be anchored at both ends as spec'd in 12.13 in order to develop yield strength of the reinforcement.

From your sketch it looks like you will have to epoxy the dowel into the (tilt up?) panel.

 

[gkm111]

Thank you Koot, that is what I assumed but didn't have an authority stating that it would be fairly negligible.

Signious, if the concrete shear strength is sufficient then there is no need to ensure that the yield strength is reached as the shear will govern.

Also shear reinforcement is only required if the factored shear force is more than 50% of the shear capacity. I'll check out A23.3 Thanks.

 

[rapt]

What shear plane are you trying to calculate the shear capacity for?

Which Canadian code formula have you quoted? The flexure formula has a Beta term in it which is conditional on reinforcement strain and moments etc. In this formula the flexural reinforcement is supposed to be fully developed past the shear plane.

 

[gkm111]

Shear plane perpendicular to panel. Ie for Wind loading. This is not for flexural reinforcement, this is simply a connection to hold the panel from in and out movement, the connection is in plane shear on the concrete and bending of the dowel.