Composite steel–concrete structures are commonly used in the field of bridges, where the steel frame provides great ease of installation, and concrete provides useful strength at low cost. This construction system makes it possible to seek to use each material to the best of its ability, so as to provide the entire construction system with greater savings. The purpose of this article is to be able to perform the simulation and the non-linear elastic calculation of composite steel–concrete beams through a calculation approach based on a matrix method of displacements. The numerical calculation model developed is based on taking into account the non-linearity of materials, or a set of laws allowing the modeling of the nonlinear behaviors of materials under an instantaneous and monotonous loading increasing until the ruin; the concrete is represented in its post-elastic part by a softening branch in compression and the contribution of the concrete stretched between two successive cracks is taken into account. Steel is represented by a perfect elastoplastic law or an elastoplastic law with firming. The proposed approach has been implemented on the Fortran programming language, where our procedure of numerical modeling of the mechanical behavior seems capable of correctly simulating the three-dimensional nonlinear behavior of isostatic and hyperstatic composite steel–concrete beams, under monotonous (increasing) static loading until ruin. It was validated by comparing the results of our calculations to experimental results or to analytical solutions.

钢-混凝土复合结构通常用于桥梁领域，在该领域中，钢框架提供了极大的安装便利性，而混凝土则以低成本提供了有用的强度。该构造系统使得能够力求最大程度地使用每种材料，从而为整个构造系统提供更大的节省。本文的目的是通过基于位移矩阵方法的计算方法，能够进行钢-混凝土组合梁的模拟和非线性弹性计算。所建立的数值计算模型是基于考虑材料的非线性或一组允许对瞬时和单调载荷增加直至破坏的材料的非线性行为进行建模的定律而建立的；混凝土在其后弹性部分中由压缩中的软化分支表示，并且考虑了在两个连续裂缝之间拉伸的混凝土的贡献。钢材表现为完美的弹塑性定律或具有牢固性的弹塑性定律。所提议的方法已在Fortran编程语言上实现，在该模型中，我们对机械行为进行数值建模的过程似乎能够正确地模拟单调（增加）静态载荷下等静压和超静压复合钢-混凝土梁的三维非线性行为。直到毁灭。通过将我们的计算结果与实验结果或分析解决方案进行比较来验证这一点。