constant: the width of the cross section b = 40 cm, the bending
moment M = 400 kN?m, and the distance of reinforcement
from the tension edge 3 cm. The other parameters are assumed
as follows: depth of the section h from 60 to 140 cm and area
of reinforcement AS =20cm2
(Figs. 1–3); and h = 100 cm
and Aa from 10 to 30 cm2
(Figs. 4–6).
In Figs. 1–6 are shown at left the diagrams calculated using
the modular ratios suggested by each author, including the
cases with different modular ratios for compressed and tensile
concrete, while at right are shown, for a more significant com-
parison, the diagrams calculated by assuming a constant mod-
ular ratio n = 15 for the compressed concrete.
Analyzing the trend of the functions shows the persity and
J. Perform. Constr. Facil. 1999.13:67-75.
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FIG. 6. Analyses of Simple RC Rectangular Section Beam (b =40cm; h = 100 cm; AS = 10–30 cm2
) Subjected to Bending (M = 400
kN?m), Following Various Theories: Maximum Tensile Stress of Metal Reinforcement When Varying Cross-Sectional Area of Metal
Reinforcement
FIG. 5. Analyses of Simple RC Rectangular Section Beam (b =40cm; h = 100 cm; AS = 10–30 cm2
) Subjected to Bending (M = 400
kN?m), Following Various Theories: Maximum Compression Stress of Concrete When Varying Cross-Sectional Area of Metal
Reinforcement
particular features of each method. First of all, it appears evi-
dent that the values in the stress diagrams for the reinforce-
ment are much less scattered than the corresponding values in
the stress curve for the concrete.
In the stress diagram referring to the reinforcement, using
the verification methods adopted by L. Lefort, W. Ritter (Ritter
1), and M. von Thullie (phase I), the stresses are clearly very
low by comparison with the mean trend of the functions, be-
cause of the contribution of the concrete subjected to tensile
stress.
For the other verification methods, the values of the stresses
of metal reinforcement can be brought together within a band
including variations between maximum and minimum stresses
of 20–30% for a section of the same depth. This is a very low
value, considering the substantial differences between the var-
ious theories.
For the concrete, on the other hand, the differences emerg-
ing between the maximum and minimum stresses for the same
height of section can reach as high as 60%.
It is also interesting to analyze the upper limits of the curves
identifying the maximum allowable stress conditions accord-
ing to the various authors. The limits for the reinforcement
were considered as varying from 100 to 120 MPa, whereas
the stresses considered as allowable for the concrete varied
from 25 to 60 MPa, depending on the authors and their re-
spective procedures.
It can also be said that the stresses considered as ‘‘allowa-
ble’’ by the various authors should not be intended as guar-
anteed limits in relation to the ultimate strength values of the
material, but generally as ranges of validity for the method
involved, in the sense that, in excess of said stress values, the
calculation method was no longer reliable.
A dimensionless representation of the verification methods
that may allow for a design of the section subjected to bend-
J. Perform. Constr. Facil. 1999.13:67-75.
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