Calculation of the geometric and mechanical quantities, minimum and maximum, according to EHE-08 (42.3.5 - Spanish regulation), without active reinforcement.

• The quantity is the amount of steel in a piece of reinforced concrete. It is possible to evaluate it globally or in certain sections of the piece.
  
  
• Usually it is measured as a percentage of steel in relation with the total piece section, although sometimes it is referenced to the effective section.
  
  
• The justification for minimum geometric quantities is: mainly constructive in columns as structural mostly compressed elements, and to control cracking due to imposed deformations produced by temperature and shrinkage, in fully or partially tensioned members. (EHE-08, 42.3.5-comments).
  
  
• The imposed deformations control is achieved with the minimum quantites, even in elements subjected to external actions or when shrincage and temperature stesses had been considered in the calculation.
  
  
• The regulation limits the maximum mechanical quantity only in the case of simple or compound compression.
  
  

Geomeric quantity parameters:				Mechanical quantity parameters:
Type of element:	ColumnBeamOwS:Nerve OwS: Distribution reinforcementSlab Foundation or fund. slabWall			Working method:	FlexionAxial
Height		m		Concrete: fck =		N/mm2
Width =		m		Axial Nd=		kN
Reinforcement:
fyk =	400500	N/mm2
Diameter: ø	68 10121416202532 40	mm
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000000000000000000000

Minimal geometric quantity. Results:
Quantity =	4	‰
Steel area =	13.2	cm2
Num. of bars =	12	ø 12
Active reinforcement can take into account only if it acts before the development of thermal or rheological deformations
Minimal mechanical quantity. Results:
fct,m =	2.8965	MPa		EHE-08, 39.1 (*1)
Compression at each face:(*2)
fyc,d =	347.83	N/mm2		EHE-08, 42.3.3	fyc,d = fyd ≤ 400 N/mm2
Steel area =	1.4375	cm2		EHE-08, 42.3.3
Num. of bars =	2	ø 12
Traction at each face:
Steel area =	13.7401	cm2		EHE-08, 42.3.4
Num. of bars =	13	ø 12
Maximum mechanical quantiy. Results:
Compression at each face:(*2)
Steel area =	94.875	cm2		EHE-08, 42.3.3
Num. of bars =	84	ø 12
(*1) This formula differs if fck is less or more than 50 MPa. (*2) For composed compression it can be made two calculations, each with compression on each side.
(*) The safety factors of materials have been considered according to EHE-08, 15.3: Yc = 1,5. Ys = 1,15.
(**) The minimum and maximum reinforcements distance should be verified according to the regulation.

• It is arguable whether to assess the quantity is required to consider the percentage of steel compared to the total section including steel and concrete, or if it has to subtract the portion of that section occupied by steel bars. In the author's opinion, the regulation always referres to the percentage of steel into the total section of the piece including steel and concrete, as it is usually considered for ease of calculation. In any case, because in general the amount of steel is small in relation with concrete, the difference between the two considerations is usually not important.
  
  
• Although for the mechanical quantity the steel reduction factor is required, and it is different for permanent or temporary situation and accidental situation (EHE-08, 15.3), the author considered that the minimum quantity is for normal work situation of the element.
  
  
• The comments show a simplified formula for rectangular sections, and a reduction factor of the minimum quantity, which do not correspond with the formulation of the articles. These expressions are inherited from the EHE-98 in which the minimal mechanical quantity was Asfyd> 0.25 fcd W1 / h. From this expression we can deduce that As > 0.041666 Acfcd / fyd, but not from the EHE-08 formulation.
  
  
• The author couldn't find out how the value of the reduction factor alpha for rectangular sections is obtained from the general formula, since the factor 1.95 * 6 = 11.7 is obtained, rather than 12.5 (missing factor 1.25 / 1.17 of its origin is unknown). It does not seem likely to be a typo, since the same formulation was already in the EHE-98. For this reason, this program uses the specific formula for rectangular sections. It should be noted that this factor alpha is located at the comments, which are not mandatory.
  
  

Version 25/06/2012