This work aims to evaluate the influence of the main parameters related to the deformability of reinforced concrete columns in the design of pin-ended rectangular slender columns, under combined bending and axial force. For this, the objective is to analyse the influence of the elasticity modulus of the concrete and the type of coarse aggregate on the deformability of slender columns and consequent dimensioning, and to propose an adaptation of the parabolic law, inserting the influences of the coarse aggregate and the initial tangent modulus of elasticity in this equation, being able to use it to evaluate the local second order effects. Concrete characteristic strengths in the range 20–50 MPa (Group I) and 55–90 MPa (Group II) and CA-50 steel $({\mathit{f}}_{\mathit{y}\mathit{k}}=500\mathbf{M}\mathbf{P}\mathbf{a})$ and their respective constitutive laws are considered. Geometric non-linearity is defined from the exact solution of the second-order differential equation for two simultaneous loading cases: geometric imperfection of the column axis and equal moments applied at its extremities. Physical non-linearity is defined from the moment–curvature diagram of the cross-section under the action of the compression force. The constitutive laws used in this diagram are: the bilinear law with horizontal threshold for steel, and for concrete in compression, the parabola-rectangle diagram on the dimensioning of the cross-section at the ultimate limit state under combined bending and axial force, and the law given in MC-90, MC-2010 [13], EC2-2010 [17] and in the Brazilian Bridge Standard ABNT NBR 7187 [20]. It is also examined the parabola of degree $\mathit{n}$, corrected for the local physical non-linearity consideration (i.e. of the column’s length). These laws explicitly or implicitly include the modulus of elasticity of concrete and the type of aggregate in it, through the factor ${\mathit{\alpha }}_{\mathit{e}}$ defined in ABNT NBR 6118 [14]. The concrete strength in tension is disregarded in this work, that is, the tension-stiffening effect for the cracked column is taken equal to zero, which is on the safe side in case of slender columns, as its cracking moment increases with increasing axial compression force. Besides, this strength depends also on the height of the cross-section, frequently considered in prestressed beams. Another important parameter, besides the concrete characteristic strength, is the geometric ratio of the total reinforcement. Thus, it is possible to determine more precisely and securely the second order effect of the slender column, and the consequent variation in reinforcement in relation to the basic case in which ${\mathit{\alpha }}_{\mathit{e}}=1$. The results showed that the influence of the type of aggregate can be considered irrelevant for the determination of reinforcement of columns with low slenderness. However, for columns with high slenderness and high strength concrete, the type of aggregate had a significant influence on the design of these columns, where the column with aggregate ${\mathit{\alpha }}_{\mathit{e}}=0,7$ required twice the reinforcement compared to the column with aggregate ${\mathit{\alpha }}_{\mathit{e}}=1$. In addition, a parabolic law adapted to analyse the second order effects of slender columns is proposed with the replacement of ${\mathit{f}}_{\mathit{c}\mathit{k}}\mathrm{b}\mathrm{y}{\propto }_0\bullet {\mathit{\alpha }}_{\mathit{e}}\bullet {\mathit{f}}_{\mathit{c}\mathit{d}0}$.

本工作旨在评估与钢筋混凝土柱的变形能力相关的主要参数在弯曲和轴力联合作用下对销端矩形细长柱设计的影响。为此，目的是分析混凝土的弹性模量和粗骨料类型对细长柱的变形能力和随之而来的尺寸的影响，并提出抛物线定律的适应性，插入粗骨料的影响以及该方程中的初始切线弹性模量，可以使用它来评估局部二阶效应。混凝土特征强度范围为 20-50 MPa（I 组）和 55-90 MPa（II 组）和 CA-50 钢$({\mathit{F}}_{\mathit{是}\mathit{克}}=500\mathbf{米}\mathbf{磷}\mathbf{一种})$并考虑了它们各自的构成规律。几何非线性由二阶微分方程的精确解定义，用于两个同时加载的情况：柱轴的几何缺陷和施加在其末端的相等力矩。物理非线性由压缩力作用下横截面的弯矩图定义。该图中使用的本构法则是：钢的具有水平阈值的双线性法则，受压混凝土，在弯曲和轴力联合作用下极限状态下横截面尺寸的抛物线矩形图，以及MC-90、MC-2010 [13]、EC2-2010 [17] 和巴西桥梁标准 ABNT NBR 7187 [20] 中给出的法律。还考察了度的抛物线$\mathit{n}$，针对局部物理非线性考虑（即列的长度）进行了校正。这些定律明确或隐含地包括混凝土的弹性模量和其中的骨料类型，通过因子${\mathit{\alpha }}_{\mathit{电子}}$ABNT NBR 6118 [14] 中定义。在这项工作中，混凝土的受拉强度被忽略，即开裂柱的拉力加强效应取为零，这在细长柱的情况下是安全的，因为它的开裂力矩随着轴压的增加而增加力量。此外，该强度还取决于横截面的高度，这在预应力梁中经常被考虑。除了混凝土特征强度外，另一个重要参数是总钢筋的几何比。因此，可以更精确、更安全地确定细长柱的二阶效应，以及由此产生的与基本情况相关的钢筋变化${\mathit{\alpha }}_{\mathit{电子}}=1$. 结果表明，可以认为骨料类型的影响与低细长柱钢筋的确定无关。然而，对于高细长、高强混凝土的柱子，骨料的类型对这些柱子的设计有很大的影响，其中骨料的柱子${\mathit{\alpha }}_{\mathit{电子}}=0,7$ 与骨料柱相比，需要两倍的钢筋 ${\mathit{\alpha }}_{\mathit{电子}}=1$. 此外，提出了一种适用于分析细长柱二阶效应的抛物线定律，并替换了${\mathit{F}}_{\mathit{C}\mathit{克}}\mathrm{乙}\mathrm{是}{\propto }_0\bullet {\mathit{\alpha }}_{\mathit{电子}}\bullet {\mathit{F}}_{\mathit{C}\mathit{d}0}$.