a basic idea of prediction of the shear strength of reinforced concrete members

1. PREDICTION OF SHEAR
STRENGTH OF REINFORCED
CONCRETE MEMBERS
presented by
Panchi Barhai
(Jorhat Engineering College)

2. INTRODUCTION
Prediction of Shear Strength of Reinforced Concrete : why is it important?
Because Reinforced Concrete –
• Develops diagonal tensile stresses
• Leading to formation of cracks
• Once formed these cracks would propagate
• Eventually shear failure would occur; abruptly.
 so ever since the invention of reinforced concrete, its strength in shear is
given due importance.
Fig. 1: Shear failure in Reinforced Concrete beam

3. Objective of this study
Refinements over the
years
To analyze the various
theories of prediction
of shear strength of
reinforced concrete
members

4. A LOOK INTO THE ORIGINAL THEORIES
First theories of prediction of shear strength of RC members :
 Ritter (1899) and Morsch (1908)
● Based on truss analogy
● Parallel chords and web members were connected by pin joints
● shear reinforcement (stirrups) represented the tensile web members
● Concrete compressive struts were inclined at 45° with respect to the
longitudinal axis of the beam
Fig. 2: Ritter and Morsch’s original truss model

5. STRUT AND TIE MODEL (STM)
 Laid by Ritter (1899) which was
later expanded by Morsch (1908).
● Concrete struts carry compressive
forces and longitudinal
reinforcements carry tensile forces as
well the stirrups.
● the truss model may be considered
as a statically determinate simple
truss.
● Stirrups when closely placed
transforms the simple truss into a
statically indeterminate truss (Fig.
3b).
Fig. 3: Morsch’s expanded model

6. American Concrete Institute (ACI) shear design philosophy

● but considered a concrete contribution term 𝑽 𝒄
𝑽 𝒔 =
𝑽 𝒖
∅
− 𝑽 𝒄
where, 𝑽 𝑺 is nominal shear strength provided by shear reinforcement
𝑽 𝒖 is factored shear force at section
ϕ is strength reduction factor
𝑽 𝒄 is nominal shear strength provided by concrete
● In computing 𝑽 𝒄, the effect of axial tension or compression were not
considered.
● Overestimated the detrimental effect of tension on shear strengths
● Overestimated the beneficial effects of compression.
Basis • Truss model by Morch (1908)

7.  Theory of Leonhardt and Walther
● angle between the compression strut and the axis of the
member, θ, is less that 45°.
 Compression field theory by Mitchell and Collins
● Developed in 1974.
● Introduced compatibility, equilibrium and stress-strain relationships.
● Determined the angle of inclination, θ.
Assumptions:
● after cracking, concrete carries no tension
● the shear is carried by a field of diagonal compression
Relationship between 𝝐 𝑿, 𝝐 𝟐 and 𝝐 𝒀 and θ
𝒕𝒂𝒏 𝟐 𝛉 =
𝝐 𝑿+𝝐 𝟐
𝝐 𝒀+𝝐 𝟐
Where, 𝜖 𝑋 = longitudinal strain in the web
𝜖 𝑦 = transverse tensile strain in the web
𝜖2 = principal compressive strain

8. MODIFIED COMPRESSION FIELD THEORY BY VECCHIO
AND COLLINS
 developed in 1986
 Refinement over CFT
 CFT ignored tension in the cracked concrete
 whereas MCFT model took into account tensile stresses in the
concrete between the cracks,
 and employed experimentally verified average stress-average strain
relationships for the cracked concrete.
• A software called Membrane -2000 is used to find the shear
strength of a reinforced concrete element in MCFT
• local stress conditions at crack locations also paid attention to.

9. a. Stress applied to a cracked element
b. calculated average stresses c. local stress at a crack
Fig. 4: Comparison of local stress at a crack with calculated average stress

10. SIMPLIFIED MODIFIED COMPRESSION FIELD THEORY BY
BENTZ, VECCHIO AND COLLINS
 Developed in 2006
 Simplified version of the MCFT.
 Accuracy is same as the MCFT
• A full load-deformation analysis is not needed always; rather, a quick
calculation of shear strength by simplified MCFT seems to be less time and
effort consuming.

11. ARTIFICIAL NEURAL NETWORK(ANN)
 Computational model
 Based on the structure and functions of biological neural networks.
 Composed of many artificial neurons or processing elements
 They are linked together according to a specific network
architecture.
 Information that flows through the network affects the structure of
the ANN because a neural network changes in a sense based on that
input and output.

12. Fig. 5: Architecture of ANN model
Neurons
Input neurons - receive stimuli from outside
the network
Output neurons - outputs are used
externally
Hidden neurons-receive stimuli from
other neurons and whose output is a
stimulus for other neurons

13.  WORKING OF ANN :
• The input to a neuron from another neuron is obtained by multiplying the
output of the connected neuron by the synaptic strength of the connection
between them.
• The artificial neuron then sums up all the weighted inputs coming to it.
𝑥𝑗 = 𝑖=1
𝑚
𝑤𝑖𝑗 𝑜𝑖
where 𝑥𝑗 is the summation of all the inputs for neuron j
𝑤𝑖𝑗 is the synaptic strength between neurons i and j
𝑜𝑖 is the output of neuron i
m is the total number of neurons sending input to neuron j.
• With every new case, ANN works better.

14. COMPARISION OF ANN WITH OTHER METHODS BY A.
SANAD AND M.P. SAKA
 The ten input parameters used were:
1. cylindrical concrete compressive strength (𝑓𝑐ˊ)
2. reinforcement ratio of horizontal tensile steel(𝜌ℎ)
3. reinforcement ratio of total horizontal steel (𝜌ℎ𝑡)
4. reinforcement ratio of transverse steel (𝜌 𝑣)
5. shear span (a)
6. effective span of the beam (L)
7. effective depth of the beam (d)
8. Beam width (𝑏 𝑤)
9. yield strength of horizontal steel (𝑓𝑦ℎ)
10. yield strength of vertical steel (𝑓𝑦𝑣)
 The output parameter was the ultimate shear strength.

15. (a) Strut and Tie method, (b) ACI method, (c) Man Hsu method and (d) Neural
Network method [7]

16.  It was found that the average ratio of actual and predicted shear strength was
0.99 for the ANN, 2.08 for the ACI method, 0.85 for the strut and tie method
and 0.84 for the Mau-Hsu method.
 Thus the ANN proved its accuracy and efficiency.
 ANN is generally used in cases where what has happened in past is repeated
almost exactly the same way.

17. SHEAR STRENGTH PREDICTION OF RC BEAMS BY
IS456(2000)
 Paper presented Ramadass Sand and Job Thomas in 2013
 Observation:
● Shear strength predicted by IS456(2000) deviated widely from
the shear strength found out experimentally.
 Conclusion:
● Indian Codes need modification for realistic prediction of
shear strength.

18. CONCLUSION
 From the simple theory of truss analogy to the development of Artificial
Neural Network, there has been tremendous positive growth in the theories.
 It is observed that every decade provided with new developments and
refinements in existing theories of shear strength of reinforced concrete
members.
 Several other researches are undergoing which are expected to bring
remarkable changes in the existing theories.

19. REFERENCES
[1] Ritter, W., “Die Bauweise Hennebique (Construction Techniques of
Hennebique),”Schweizerische Bauzeitung, Zürich, V. 33, No. 7, Feb. 1899, pp. 59-61.
[2] E. Morsch, “Seine Theorie und Anwendung" (Reinforced Concrete Theory and
Application) , Der Eisenbetonbau, Konrad Wittwer Verlag, Stuttgart,1908
[3] ACI, "Standard Building Regulations for the Use of Reinforced Concrete" American
Standard Specification No. 23, Vol. 16, Feb. 1920, pp. 283-322.
[4] D. Mitchell and M. P. Collins, "Diagonal Compression Field Theory – A Rational
Model for Structural Concrete in Pure Tension", ACI Journal, Proceedings, Vol. 71, No. 8,
Aug.1974, pp. 396-408
[5] Vecchio, F. J.; and Collins, M. P., “The Modified Compression Field Theory for
Reinforced Concrete Elements Subjected to Shear,” ACI JOURNAL, Mar.-Apr. 1986
[6] Bentz, E.C; Vecchio, F. J.; and Collins, M. P., “Simplified Modified Compression Field
Theory for Calculating Shear Strength of Reinforced Concrete Elements,” ACI Structural
Journal, July.-Aug. 2006
[7] Sanad, A; and Saka, M.P., “Prediction of Ultimate Shear Strength of Reinforced-
Concrete Deep Beams Using Neural Networks” ACI Structural Journal, July 2001