About modeling long-span structure with joints with small gaps under seismic loads

Introduction

When modeling unique buildings and structures, we encounter the necessity to account for the real operational scheme of the structure, faithfully reproduce the construction itself, its properties, taking into account initial imperfections, and the actual scheme of work of the joints, rather than an idealized one.

In the current article, we will examine one of the numerical modeling approaches for the operation of joints, the structural design of which allows for clearances or gaps, resulting in the structure being able to move freely within limited distances.

Description of the Structure

The large-span structure is located in a seismic area. The seismicity rating of the construction site is assessed at 9 points. According to geophysical research, the refined seismicity of the construction site is 8 points. The object consists of a building with a complex geometric shape, featuring an outstanding cantilevered open terrace measuring 35.2 meters in length. The building's roof is designed as a truss spatial steel structure, supported by steel supporting components, with overhanging edges on all sides and a canopy extending over the main entrance and the terrace. Around the above-ground reinforced concrete part of the framework, there is a structure known as a steel "Clip," which represents a spatial truss structure.

The approximate dimensions in plan are 124.8 x 207.0 meters. The supporting components, which connect the steel roof structures and facades with the reinforced concrete structures of the operational part of the facility, are designed as hinge movable and fixed joints with clearances/gaps along the normal to the base of the joint. Based on preliminary calculations using the linear-spectral theory, it was determined that, in addition to compressive reactions, tensile forces may occur in the joints, leading to cyclic opening/closing of the clearance and essentially causing multi-directional impact. Assessing the contribution of the dynamic impact component to the overall stress-strain state of the structure and joints within the framework of linear-spectral theory is impossible. Considering this, experimental modeling of the structure was performed in a dynamic setup using direct integration of dynamic equations over time with an implicit scheme, taking into account physical, geometric, and structural nonlinearities.

Structural model

The analysis of the structure's behavior was performed in a transient dynamic setup using the Newmark method. Damping was implemented in the analytical model using Rayleigh damping. For steel structures, the determination of the "alpha" and "beta" parameters was performed with damping set at 2% of critical damping, for reinforced concrete it was set at 5% of critical damping.

The modeling of joints was done using discrete spring elements COMBIN39. The behavior of the supporting joints with clearances was represented in the form of a three-linear displacement-stiffness diagram. The stiffness of the extreme segments was equivalent to the longitudinal stiffness of the connected structures, while the middle segment was assumed to have the stiffness of disc springs introduced into the structural node to reduce the influence of clearances on the stress-strain state of the structure.

Figure below displays a graph of force verification in the element relative to the displacement of one of the structure's nodes. In the 0-2 interval, a compressive load is applied to the node, followed by unloading. In the 2-3 interval, a displacement equal to the clearance is applied, followed by equivalent tensile loading in stage 1.

Results

The conducted computational studies indicate that small clearances/gaps in the joints, allowing limited movement of the structure as a rigid body, have a minimal impact on the resulting stress-strain state of the entire system.

According to the performed computational studies, the joints with clearances have relations describing the stress-strain state over time that are similar to those of the model without them.

Some joints only work in compression, while others experience momentary detachments accompanied by dynamic impact. Such dynamic loading of the system does not qualitatively affect the overall deformation over time, but it leads to local rapidly decaying high-frequency oscillations (visible in the graphs as local densifications of the deformation curves).

In most cases, the amplitude of compression/detachment forces is close to those obtained from the model without accounting for the behavior of joints with clearances. For certain elements with initially small support reactions the detachment forces increase from 8% to 37%, but limit of strength has not been reached.