Calculation of the maximum efforts of the reinforced concrete section to bending and axial. Generating of the interaction diagram, both according to the parable-box diagram as the rectangular digram of the concrete, and the strain domains diagram, according to the EHE-08.

• The interaction diagram of the concrete section is developed according to EHE-08, with the behavior of concrete specified in Article 39.5, following both the parable-box diagram as the rectangular stress-strain diagram of the concrete. In this interaction diagram, the combination of the maximum axial and bending moments of the section is obtained from the maximum deformation that admits the section, according to the diagram of deformation domains described in Article 42.
  
  
• The domain deformation diagram is generated from the maximum admissible deformation of concrete and steel, when considering the neutral axis moving from -∞ to +∞.
  
  
• The interaction diagram is obtained by calculating for each position of the neutral axis, the balance of forces and moments about the midpoint of the concrete section.
  
  
• The forces and moments of the reinforcements are calculated by adding each steel bar. The forces and moments of the concrete are calculated based on the compressed concrete area from the parabola-rectangle diagram and the rectangular diagram.
  
  
• The domain deformation diagram is as follows:
  
  
  
  

Parameters:
Materials:
Concrete: fck =	.2530354045 505560708090100.	N/mm2
Concrete deduction factor Yc =				Yc = 1.5 except in accidental situation (Yc = 1.3), fatigue or fire (EHE-08, 15.3)
Compression fatigue factor αcc =		(*1)		Usually αcc = 1 (in EHE-98 αcc = 0.85)
Steel: fyk =	.400500.	N/mm2		Ys = 1.15 except in accidental situation (Ys = 1.0), or intense control (Ys = 1.10) (see EHE-08, 15.3)
Steel deduction factor Ys =
Steel elasticity modulus Es =		N/mm2		Usually Es = 200,000 N/mm2 (EHE-08, Art. 38.8 and comments at Art. 38.4)
Section:
Width (máx. 2000) =		mm
Height (máx. 2000) =		mm
Top nominal cover =		mm
Bottom and sides nominal cover =		mm
Renforcement:
Styrrup: ø =	.There aren't681012 1416202532 40.	mm(*2)
Top reinforcement:		ø	.681012 1416202532 40.	mm
Bottom reinforcement:		ø	.681012 1416202532 40.	mm
Lateral reinforcement (each side):		ø	.681012 1416202532 40.	mm(*3)
Check point:
Neutral axis depth:		mm		(For results in a specific point of the charts)
Draw parable-box diagram:	Sí
Draw rectangular diagram:	Sí
(*1)The fatigue factor reflects this effect in concrete, when subjected to high levels of compression due to long-term loading. It is generally adopts αcc = 1, although the author of the project should consider its reduction to 0.85, if the permanent and total loads ratio is high, or depending on the characteristics of the structure (EHE-08, 39.4)
(*2)The regulation allows to reduce the bending radius in hoops or stirrups less or equal to 12 mm diameter, which is recommended not to use larger diameter bars, being preferable to place double or triple styrrups if required. (EHE-08, 69.3.4).
(*3)The side reinforcement introduced is considered in the calculation. If you do not want to consider it resistant for allocating its mechanical capacity to horizontal deflections, or for any other reason, you should not enter it into the program. However, it must be verified that reinforcements separations specified in the regulations are met (it can be used the "Aggregate and rebar gaps" utility)
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Results:
Materials:
Elastic steel deformation =	2.5	‰
Concrete compressive strength fcd =	20	N/mm2		(EHE-08, 39.4)
Break strain at simple compression εc0 =	2	‰		(EHE-08, 39.5)
Ultimate flexural strain εcu =	3.5	‰		(EHE-08, 39.5)
Concrete parable-box diagram:
Grade of parable n =	2			(EHE-08, 39.5)
Highest traction =	-699.35	kN, con	0	mkN
Maximum simple bending moment =	Value visible only to users with an active subscription. (+info)
Maximum moment combined with axial =	522.95	mkN	2183.16	kN
Highest compression =	5443.4	kN, con	0	mkN
Rectangular concrete diagram:
η =	1			(EHE-08, 39.5)
λ =	0.8			(EHE-08, 39.5)
In Checkpoint: η(50) =	1			(EHE-08, 39.5)
In Checkpoint: λ(50) =	0.07			(EHE-08, 39.5)
In Checkpoint: rectangle area(50) =	0.8	kN/mm		(EHE-08, 39.5)	A = [λ(50) * h] * [η(50) * fcd]
In Checkpoint: Force(50) =	320	kN		(EHE-08, 39.5)	F = A * b
In Checkpoint: Bending moment(50) =	89.6	mkN
Highest traction =	-699.35	kN, con	0	mkN
Maximum simple bending moment =	Value visible only to users with an active subscription. (+info)
Maximum moment combined with axial =	530.46	mkN	2157.47	kN
Highest compression =	5443.39	kN, con	0	mkN
Interaction diagram:

• These calculations proposed by the regulation are very accurate and instructive, but in the author's opinion, its accuracy is dissolved in practice when sizing elements with load increment factors of a magnitude order as high as the current 1.35 and 1.5.
  
  
• In concrete sections with unsymmetrical reinforcements or covers, the balance in pure traction or compression at both extremes is not reached, appearing moments in axial extreme values​​.
  
  
• Although at the EHE 08 the fatigue factor has increased by around 17% compared to the EHE 98 (from 0.85 to 1), the maximum resistant efforts of the section are not increased this percentage, but at much lower percentages. In fact it has been observed that in some cases the maximum tension stress and the maximum bending moment are reduced. With this it seems that to make the calculations with the fatigue factor as EHE-98 is not in all cases on the safety side.
  
  

Version 15/11/2012