The available standards, such as EN 1991-1-4 [1], ASCE/SEI 7-16, and NBC 2015 presented wind load parameters such as wind pressure coefficient (Cp) for basic shapes. The important point is how to calculate wind load parameters faster and more accurately rather than working on time-consuming as well as sometimes complicated formulas in standards.
In the current validation example, we investigate wind force coefficient (Cf) of cube shapes with EN 1991-1-4 [1]. There are three dimensional cases that we will explain more about if in the next part.
The model is based on the example 4 of [1]: Point-supported slab.
The flat slab of an office building with crack-sensitive lightweight walls is to be designed. Inner, border and corner panels are to be investigated. The columns and the flat slab are monolithically joined. The edge and corner columns are placed flush with the edge of the slab. The axes of the columns form a square grid. It is a rigid system (building stiffened with shear walls).
The office building has 5 floors with a floor height of 3.000 m. The environmental conditions to be assumed are defined as "closed interior spaces". There are predominantly static actions.
The focus of this example is to determine the slab moments and the required reinforcement above the columns under full load.
A thin plate is fixed on one side and loaded by means of distributed torque on the other side. First, the plate is modeled as a planar plate. Furthermore, the plate is modeled as one-fourth of the cylinder surface. The width of the planar model is equal to the length of one-fourth of the circumference of the curved model. The curved model thus has almost equal torsional constant to the planar model.
A cantilever of I-profile is supported on the left end and it is loaded by the torque M. The aim of this example is to compare the fixed support with the fork support and to investigate the behaviour of some representative quantities. The comparison with the solution by means of plates is also made. The verification example is based on the example introduced by Gensichen and Lumpe.
A pipe with a tubular cross-section is loaded by internal pressure. This internal pressure causes axial deformation of the pipe (the Bourdon effect). Determine the axial deformation of the pipe endpoint.
In the current validation example, we investigate wind pressure value for both general structural designs (Cp,10) and cladding or façade design (Cp,1) of rectangular plan buildings with EN 1991-1-4 [1]. There are three dimensional cases that we will explain more about if in the next part.
A thin circular ring of a rectangular cross-section is exposed to external pressure. Determine the critical load and corresponding load factor for in-plane buckling.
A quarter-circle beam with a rectangular cross-section is loaded by means of an out-of-plane force. This force causes a bending moment, torsional moment, and transverse force. While neglecting self-weight, determine the total deflection of the curved beam.
A strut with a circular cross-section is supported according to four basic cases of Euler buckling and subjected to pressure force. Determine the critical load.
A sphere is subjected to a uniform flow of viscous fluid. The velocity of the fluid is considered at infinity. The goal is to determine the drag force. The parameters of the problem are set so that the Reynolds number is small and the radius of the sphere is also small, thus the theoretical solution can be reached - Stokes flow (G. G. Stokes 1851).
A cantilever is loaded by a moment at its free end. Using the geometrically linear analysis and large deformation analysis, and neglecting the beam's self-weight, determine the maximum deflections at the free end. The verification example is based on the example introduced by Gensichen and Lumpe.
A column is composed of a concrete section (rectangle 100/200) and a steel section (profile I 200). It is subjected to pressure force. Determine the critical load and corresponding load factor. The theoretical solution is based on the buckling of a simple beam. In this case, two regions have to be taken into account due to different moments of inertia and material properties.
The wide plate with a hole is loaded in one direction by means of the tensile stress σ. The plate width is large with respect to the hole radius and it is very thin, considering the state of the plane stress. Determine the radial stress σr, tangential stress σθ, and shear stress τrθ around the hole.
A cantilever from a rectangular cross-section is lying on an elastic Winkler foundation and loaded by distributed loading. The image shows the calculation of the maximum deflection and maximum bending moment.
The model is based on the example 4 of [1]: Point-supported slab. The internal forces and the required longitudinal reinforcement can be found the in verification example 1022. In this example, punching is examined in the axis B/2.
A cantilever is loaded by a moment at its free end. Using the geometrically linear analysis and large deformation analysis, and neglecting the beam's self-weight, determine the maximum deflections at the free end. The verification example is based on the example introduced by Gensichen and Lumpe.
A cantilever is loaded by a transversal and an axial force on the right end and is fully fixed on the left end. The problem is described by the following set of parameters. The problem is solved by using the geometrically linear analysis, second-order analysis, and large deformation analysis.
In the current validation example, we investigate wind pressure value for both general structural design (Cp,10) and local structural design such as cladding or façade systems (Cp,1) based on EN 1991-1-4 flat roof example [1] and
Japanese Wind Tunnel Data Base
. The recommended setting for three-dimensional flat roof with sharp eaves will be described in the next part.
Planar truss consisting of four sloped members and one vertical member is loaded at the upper node by means of the vertical force Fz and out of plane force Fy. Assuming large deformation analysis and neglecting self-weight, determine the normal forces of the members and the out of plane displacement of the upper node uy. The verification example is based on the example introduced by Gensichen and Lumpe.
In the current validation example, we investigate wind pressure coefficient (Cp) of flat roof and walls with ASCE7-22 [1]. In the section 28.3 (Wind loads - main wind force resisting system) and Figure 28.3-1 (load case 1), there is a table which shows Cp value for different roof angle.
A curved beam consists of two beams with a rectangular cross-section. The horizontal beam is loaded by distributed loading. While neglecting self-weight, determine the maximum stress on the top surface of the horizontal beam.
A thin rectangular orthotropic plate is simply supported and loaded by uniformly distributed pressure. The directions of axes x and y coincide with the principal directions. While neglecting self-weight, determine the maximum deflection of the plate.
A tapered cantilever is fully fixed on the left end and subjected to a continuous load q. Small deformations are considered and the self-weight is neglected in this example. Determine the maximum deflection.
In the current validation example, we investigate wind pressure coefficient (Cp) for both main structural members (Cp,ave) and secondary structural members such as cladding or façade systems (Cp,local) based on NBC 2020 [1] and
Japanese Wind Tunnel Data Base
for low-rise building with 45 degree slope. The recommended setting for three-dimensional flat roof with sharp eaves will be described in the next part.
A beam pinned at both ends is loaded with concentrated force in the middle. Neglecting its self-weight and shear stiffness, determine the beam's maximum deflection, normal force, and moment at the mid-span, assuming the second- and third-order analysis.
A beam is fully fixed (warping is restricted) on the left end and supported by a fork support (free warping) on the right end. The beam is subjected to a torque, longitudinal force, and transverse force. Determine the behavior of the primary torsional moment, secondary torsional moment and warping moment. The verification example is based on the example introduced by Gensichen and Lumpe (see reference).
A simple oscillator consists of mass m (considered only in the x-direction) and linear spring of stiffness k. The mass is embedded on a surface with Coulomb friction and is loaded by constant-in-time axial and transverse forces.