Slender structures are elegant aesthetically. The insufficiency in knowledge of the real resistance to buckling of very slender reinforced concrete columns leads to an exaggeration of the sizes of the columns. _The examples of concrete compression members cited and constructed in Industry on a global basis suggest that very slender columns have inherent safety both from the point of view of the ultimate strength and stability. The strengths of columns given. by the British codes would seem to be exceeded by many of the long slender reinforced concrete columns and struts which have been used Internationally. Both the theoretical and the experimental short term investigations have been carried out to establish the behaviour of hinged, very slender reinforced concrete columns at various stages'of axial loading. Forty three very slender reinforced concrete columns of two different square cross sections with two sizes of longitudinal reinforcements with lateral ties were cast. Slenderness rates, L A, were varied from 30 to 79. Special factors were obtained to relate the actual modulus of elasticity of concrete in columns at buckling failure to a knowledge of the initial modulus of elasticity of concrete in control cylinder specimens. Both theoretical and experimental graphs of load against moment, made dimensionless for critical sections of columns have been obtained. Dimensionless load-moment interaction diagrams using material failure as the criterion have been superimposed on these graphs to show considerable inherent material strength of the tested columns near buckling collapse failures. A theory using the fundamental approach has, been developed to predict the deflected shape and moments along the, heights of the columns at various stages of loading. The proposed theory predicts with good correlations the experimental deflections and moments of any loading stages of the columns. The theory has been used to obtain the required variables, to arrive at the initial predicted design loads of the investigated columns. Good correlations of the moments derived from observed strains have also been obtained. The developed theory predicts satisfactorily the buckling collapse loads of the columns. Although the theory has been derived for axially I loaded very slender reinforced concrete-columns, it seems to accept satisfactorily eccentricities of up to about 10 mm. This was confirmed after extensive comparisons of the theoretical buckling collapse loads with the applicable tests of other authors. Creep In the columns investigated was discovered to be one of the major factors for serious consideration. This was conclusively revealed from the observations on the last two very long term creep tests on columns. The actual safe sustained loads for these very slender columns of slenderness ratios, L/H, between 40 and 79 seem to be between 33% and 19% of the short term buckling collapse loads. The reduced modulus approach to predict the safe long term sustained loads seems to give reasonable values for L/H ratios of 40 and 50. The recommendations given for the proposed design of very slender reinforced concrete columns seem to be adequate and simple to use in practice. They are further simplified by the derivation of two equations for the reduction factors, R, for the slenderness ratios between 36 and 40 and between 40 and 79 respectively. The investigation has proved that very slender reinforced concrete columns are very dangerous structural members, as they tend to have violent buckling failures. Nevertheless, It must be prudent not to design against disaster at any cost. This Investigation seemed to have enhanced considerably knowledge of the design of very slender reinforced concrete columns.

Slender structures are elegant aesthetically. The insufficiency in knowledge of the real resistance to buckling of very slender reinforced concrete columns leads to an exaggeration of the sizes of the columns. _The examples of concrete compression members cited and constructed in Industry on a global basis suggest that very slender columns have inherent safety both from the point of view of the ultimate strength and stability. The strengths of columns given. by the British codes would seem to be exceeded by many of the long slender reinforced concrete columns and struts which have been used Internationally. Both the theoretical and the experimental short term investigations have been carried out to establish the behaviour of hinged, very slender reinforced concrete columns at various stages'of axial loading. Forty three very slender reinforced concrete columns of two different square cross sections with two sizes of longitudinal reinforcements with lateral ties were cast. Slenderness rates, L A, were varied from 30 to 79. Special factors were obtained to relate the actual modulus of elasticity of concrete in columns at buckling failure to a knowledge of the initial modulus of elasticity of concrete in control cylinder specimens. Both theoretical and experimental graphs of load against moment, made dimensionless for critical sections of columns have been obtained. Dimensionless load-moment interaction diagrams using material failure as the criterion have been superimposed on these graphs to show considerable inherent material strength of the tested columns near buckling collapse failures. A theory using the fundamental approach has, been developed to predict the deflected shape and moments along the, heights of the columns at various stages of loading. The proposed theory predicts with good correlations the experimental deflections and moments of any loading stages of the columns. The theory has been used to obtain the required variables, to arrive at the initial predicted design loads of the investigated columns. Good correlations of the moments derived from observed strains have also been obtained. The developed theory predicts satisfactorily the buckling collapse loads of the columns. Although the theory has been derived for axially I loaded very slender reinforced concrete-columns, it seems to accept satisfactorily eccentricities of up to about 10 mm. This was confirmed after extensive comparisons of the theoretical buckling collapse loads with the applicable tests of other authors. Creep In the columns investigated was discovered to be one of the major factors for serious consideration. This was conclusively revealed from the observations on the last two very long term creep tests on columns. The actual safe sustained loads for these very slender columns of slenderness ratios, L/H, between 40 and 79 seem to be between 33% and 19% of the short term buckling collapse loads. The reduced modulus approach to predict the safe long term sustained loads seems to give reasonable values for L/H ratios of 40 and 50. The recommendations given for the proposed design of very slender reinforced concrete columns seem to be adequate and simple to use in practice. They are further simplified by the derivation of two equations for the reduction factors, R, for the slenderness ratios between 36 and 40 and between 40 and 79 respectively. The investigation has proved that very slender reinforced concrete columns are very dangerous structural members, as they tend to have violent buckling failures. Nevertheless, It must be prudent not to design against disaster at any cost. This Investigation seemed to have enhanced considerably knowledge of the design of very slender reinforced concrete columns. / Scientific Research Council

Aujourd’hui, la technologie du béton ayant fortement évolué, il est, sous certaines conditions, réaliste de construire des éléments structuraux en béton ayant à la compression une résistance de 90N/mm² voire nettement plus. En conséquence, l’ingénieur concepteur peut être amené dans le cadre du dimensionnement des colonnes à en diminuer les dimensions transversales pour des raisons esthétiques ou d’encombrement. Inévitablement, cette diminution de la section transversale induit une augmentation de l’élancement et augmente ainsi les risques des instabilités de flambement. A cette question de flambement, il faut adjoindre l’influence d’une préconception qui veut qu’une structure en béton à haute résistance soit moins ductile qu’une structure construite avec un béton normal ! De ceci résulte la question à la base de ce travail : « Peut-on arriver à diminuer la section transversale d’une colonne en utilisant des résistances de béton plus élevées tout en imposant la même valeur de capacité portante et en ne réduisant pas leur ductilité ? » Afin de répondre à cette question, le travail s’est articulé autour de deux axes essentiels qui sont d’une part une campagne d’essais (afin d’obtenir des résultats fiables) sur 12 colonnes en béton armé à haute résistance (90N/mm²) d’élancement 74 et 82 dont l’excentricité de la charge est une variable, et d’autre part l’implémen- tation de deux programmes informa- tiques utilisant le principe de l’analyse au second ordre en vue de réaliser une étude paramétrique dont l’excentricité, la hauteur des colonnes, la proportion d’acier, la résistance du béton sont les variables. Trop souvent encore, les ingénieurs de bureau d’études hésitent à effectuer un calcul au second ordre et placés devant la question des dimensions de section à donner à une colonne de hauteur et de capacité portante imposées, déterminent celles-ci pour se satisfaire d’un calcul au 1er ordre. Au terme de notre étude, nous avons montré que cette approche est loin d’être optimale, qu’il est possible, au prix d’un calcul au second ordre (mais il est fait à l’ordinateur), de tirer profit d’une augmentation de la résistance du béton pour réduire les dimensions des sections et aboutir en toute sécurité à un dimensionnement plus économique en consommation de matériaux (acier, béton, ciment).

Aujourd’hui, la technologie du béton ayant fortement évolué, il est, sous certaines conditions, réaliste de construire des éléments structuraux en béton ayant à la compression une résistance de 90N/mm² voire nettement plus. En conséquence, l’ingénieur concepteur peut être amené dans le cadre du dimensionnement des colonnes à en diminuer les dimensions transversales pour des raisons esthétiques ou d’encombrement. <p><p>Inévitablement, cette diminution de la section transversale induit une augmentation de l’élancement et augmente ainsi les risques des instabilités de flambement. <p>A cette question de flambement, il faut adjoindre l’influence d’une préconception qui veut qu’une structure en béton à haute résistance soit moins ductile qu’une structure construite avec un béton normal !De ceci résulte la question à la base de ce travail :<p><p>« Peut-on arriver à diminuer la section transversale d’une colonne en utilisant des résistances de béton plus élevées tout en imposant la même valeur de capacité portante et en ne réduisant pas leur ductilité ?»<p><p>Afin de répondre à cette question, le travail s’est articulé autour de deux axes essentiels qui sont d’une part une campagne d’essais (afin d’obtenir des résultats fiables) sur 12 colonnes en béton armé à haute résistance (90N/mm²) d’élancement 74 et 82 dont l’excentricité de la charge est une variable, et d’autre part l’implémen- tation de deux programmes informa- tiques utilisant le principe de l’analyse au second ordre en vue de réaliser une étude paramétrique dont l’excentricité, la hauteur des colonnes, la proportion d’acier, la résistance du béton sont les variables.<p><p>Trop souvent encore, les ingénieurs de bureau d’études hésitent à effectuer un calcul au second ordre et placés devant la question des dimensions de section à donner à une colonne de hauteur et de capacité portante imposées, déterminent celles-ci pour se satisfaire d’un calcul au 1er ordre. Au terme de notre étude, nous avons montré que cette approche est loin d’être optimale, qu’il est possible, au prix d’un calcul au second ordre (mais il est fait à l’ordinateur), de tirer profit d’une augmentation de la résistance du béton pour réduire les dimensions des sections et aboutir en toute sécurité à un dimensionnement plus économique en consommation de matériaux (acier, béton, ciment).<p><p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished