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genieur und Architekten Vereins, and in 1896 by Mandl with
publications in the journal Zeitschrift des O ¨ sterreichischen In-
genieur und Architekten Vereins. Melan’s method is shown in
Eqs. (22)–(24) of Gori (1999).
At the end of 19th century, in Belgium, Paul Christophe
published a method for calculating the stresses due to bending
in the Annales des Travaux publics de Belgique (Christophe
1899). This method was like that considered by Max Ritter
von Thullie for the concrete in RC members, in its second
phase (von Thullie 1896, 1897). Christophe’s proposed cal-
culation method was soon in widespread use. Von Thullie
methods, which consider also a nonlinear behavior of com-
pressed concrete, are described in detail in Eqs. (28)–(39) of
Gori (1999).
In France, Edmond Coignet and N. De Tedesco published
a method ‘‘du calcul des ouvrages en ciment arme ´ avec os-
sature metallique’’ in the Bullettin de la Socie ´te ´ des Inge ´nieurs
Civils de France (Coignet and de Tedesco 1894), summarized
in Eqs. (25)–(27) of Gori (1999), which became very popular
for its simplicity.
Again, Stellet published a work in Reveu Tecnique, and L.
Lefort in 1898 published his theories in Nouvelles Annales de
la Construction, Eqs. (40)–(43) of Gori (1999).
While Conside `re was at work in France, in SwitzerlandWil-
helm Ritter, professor of the Zurich Polytechnic, published his
theories in the Schweizerische Bauzeitung in 1899, considering
a nonlinear behavior of concrete (Ritter 1899). He proposed a
calculation method that quickly became the commonly used
in Switzerland, described in Eqs. (44)–(54) of Gori (1999).
In the same years, Franc ¸ois Hennebique developed his own
particular design method and recommended all the holders of
his patent rights in Europe to adopt it. This method was not
J. Perform. Constr. Facil. 1999.13:67-75.
Downloaded from ascelibrary.org by SHANGHAI INSTITUTE OF on 12/12/12. Copyright ASCE. For personal use only; all rights reserved.JOURNAL OF PERFORMANCE OF CONSTRUCTED FACILITIES / MAY 1999 / 69
FIG. 4. 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: Position of Neutral AxisWhen Varying Cross-Sectional Area of Metal Reinforcement
FIG. 3. Analyses of Simple RC Rectangular Section Beam (b =40cm; h = 60–140 cm; AS =20cm2
) Subjected to Bending (M = 400
kN?m), Following Various Theories: Maximum Tensile Stress of Metal ReinforcementWhen Varying Depth of Section
the outcome of any particular theory; it was the outcome of a
practical calculation procedure, in which the safety coefficients
were adapted on the basis of experience (de Tedesco and Mau-
rel 1904).
COMPARISON OF VARIOUS ANALYSIS METHODS
FOR BENDING
In the following is given a comparison between the first
methods for verifying simple bending in rectangular sections
with a single metal reinforcement position, described by Gori
(1999), to analyze the quantitative influence of the various
calculation methods on practical problems.
Firstly, a particular rectangular section concrete beam, singly
reinforced, subjected to simple bending, has been analyzed.
The diagrams of Figs. 1–6 show the values of the neutral
axis position (Figs. 1 and 4), of the maximum stresses of con-
crete (Figs. 2 and 5), and of metal (Figs. 3 and 6) in relation
to that rectangular RC section in which just one geometrical
parameter has been varied (within allowable limits) while
maintaining the other parameters constant (Gori and Simon-
celli 1994).
In all the diagrams the following parameters are assumed