Verification of the anchorage limit state

 1.5 Verification of the anchorage limit state

The method used is applicable to both flexible (v >= 2h) and stiff footings with a ratio of v/h>1.

The following is a more detailed description of the method than that found in EC2, 9.8.2.2

A θ° shear crack is assumed to be possible, as depicted in Figure 1-40 (a). Given the low bending reinforcement ratios, d may be accepted to be 0.9h and the height of the point where cracking begins, 0.9d or 0.81h. 

For the sake of simplification, the moments used in the calculations below are the moments on the column face. A 75-mm side cover is also assumed, as in footings poured onto soil .

The reinforcement anchor length should be as required to anchor the bar force from the point where the reinforcement intersects with the crack onward, i.e. point A.

(The reinforcement is assumed to be constant across the entire width.) 

Taking the moments at B 

F_sx * 0.81h = x σ_td (v -x/2) 

where 

X= v - 0.81h cotθ 

and operating, yields

In addition to the equation above and in keeping with the bending moment applied, the following must hold:

from which it follows that:

(l_b reflects bonding position I, given the position of the bars.)

1.5.1 Bond anch orage

Given x = v – 0.81h cot θ:

Since length l'_1 is in bonding position I:

and consequently

The minimum value of x is found with the maximum value of cot θ which, according to EC2, is equal to cotθ = 2.5, yielding:

x= v - 2.03h = h(v/h - 2.03)

or

x/h = v/h - 2.03 [1.14]

[1.9] is a more general expression than the formulas set out in EC2, in which critical value x is simplified to be equal to 0.5h. See the discussion below.

The graph in Figure 1-41 shows the distance x in terms of h for different values of v/h.

If v/h ≤2.5, a conservative value for x is 0.5h, as adopted in Eurocode EC2. 

Direct calculationis preferable.

KDS 24 14 21 콘크리트교 설계기준(한계상태설계법)

4.6.10.2 확대기초판

https://skyground21.tistory.com/entry/Column-and-wall-footings-Anchorage-of-bars

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