An integrated framework for nonlinear analysis of plane frames exposed to fire using the direct stiffness method

Fully coupled multi-physics nonlinear analysis of structural space frames subjected to fire using the direct stiffness method

“…A 1D beam-column element with 6 degrees of freedom (DOFs), as shown in Figure 2, is developed from the classical Euler–Bernoulli theory. As discussed in Srivastava and Prakash (2017), it is reasonable to neglect shear deformations for structural members of slenderness ratio greater than 4. It is to be noted that the DSM-based structural analysis, in which the element force–deformation relations derived from the classical beam-column theories and involves stability and bowing functions, facilitates computationally efficient formulation (Saafan, 1963).…”

“…where ε m , ε T , ε th , ε tr , and ε cr denote the mechanical strain, total thermal strain, thermal strain, transient thermal strain, and creep strain, respectively. The assumption of additive decomposition of strain is acceptable for structural fire analysis of steel and concrete structures as discussed in Srivastava and Prakash (2017). It should be noted that for thermo-elastic simulations, this formulation can be readily employed by setting ε tr = ε cr = 0 in equation (11).…”

“…Three-way sequential coupling is enforced between thermal, pore pressure, and mechanical solvers in a staggered scheme similar to the one used in Srivastava and Prakash (2017). Mechanical solvers take cross-sectional temperature and pore-pressure profiles as input.…”

“…Although equation (42) was proposed for NSC, the same relationship is assumed for high-strength concrete (HSC) due to the lack of availability of data. Parametric studies have been performed on ε tr to determine appropriate level of transient thermal strain that can be utilized in case of HSC similar to Cai et al (2003) and Srivastava and Prakash (2017). Creep strain in concrete is modeled using the empirical relationship proposed by Harmathy (1993) as…”

“…While it considers the necessary physical processes, its formulation restricts its use to only isolated structural members. Second is a recent approach by Srivastava and Prakash (2017), which developed a three-way coupled formulation based on the direct stiffness method (DSM) for analysis of plane structural frames. Their framework was the first to consider use of DSM for detailed structural fire analysis but was developed for two-dimensional (2D) structures and assumed linear thermal gradients within structural members for calculation of temperature-related member forces.…”