yield displacement of an element is defined as the displacement when the concrete strain reaches to 0.0035 . I'm looking for a valid reference (paper or book) related to this matter.your help is highly appreciated.
Measured approximately by observing the strain in the steel reinforcing and not with the concrete reaching the steel, we say that it is the displacement of yielding
By a sensor attached to the steel reinforcing prior to the concrete casting to connect it later with the strain gauge
The method of examination is available in practical research
I'm sorry to contradict you, but concrete cannot yield being a brittle material, steel and ductile metals can yield. The strain that you cite, 0.0035 is commonly considered the crushing strain (ultimate one) for concrete (see EN1992-1-1 or Model Code 90 or Model Code 2010).
The yielding displacement of a concrete member is associated to the yielding strain reached in the steel rebars fy/Es (yielding stress divided by steel modulus of elasticity) and not to the strain inside concrete.
Measured approximately by observing the strain in the steel reinforcing and not with the concrete reaching the steel, we say that it is the displacement of yielding
By a sensor attached to the steel reinforcing prior to the concrete casting to connect it later with the strain gauge
The method of examination is available in practical research
As mentioned above, the premise that the section will yield when .35% compressive strain is reached at the extreme fiber is not correct. For a purely flexural member, yielding of the section should occur when the tension reinforcement reaches yield strain. For a member under combined compression and flexure (such as a column), the concrete compressive strain WILL come into it, as it will probably reach large strains causing the section to "yield" (generally less than .35% though) before the tension reinforcement yields.
The following report from the University of Patras is quite comprehensive on the topic:
First of all 0.0035 strain will not occur in any structural concrete member subjected to two point loading. Only 90% to 95% of the 0.0035 strain will only occur. This is the experience from experiment. Also, please refer W.G.Corley (1966).
The yield displacement or deflection of a structural concrete member corresponds to the yield strain of tensile reinforcement. If the electrical resistance strain gauges pasted in the tension steel before the casting throughout the constant bending moment region with the spacing at least 100 mm to 150 mm spacing, then we can monitor the yield strain. If not, we cannot observe it. The deflection/displacement corresponds to the yield strain of tension steel is the deflection/displacement of a structural concrete member subjected flexure.
Dear Hamed Dabiri , first the ultimate strain of concrete is assumed to be near to 0.35%, this means that you are not near the yielding, you are on the maximum compression strain of the concrete before failure. Just as a comment the maximum concrete strain in compression of concrete in ACI 318 is just 0.3%. As other people in this post mention, for a member in pure flexure, the reinforcement should be provided in order that the material that will first yield will be the steel and not the concrete, even if you have compression force mix with bending moments you may try to find an arrangement in your reinforcement that produces first the yield of steel and not the concrete, you can study this problem quite good in a moment curvature diagram. Find in the following link some material about related to lecture notes of MIT 1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004