In this verification example the punching shear resistance of an inner column of a flat slab is examined. The column has a circular secton with a 30cm diameter.
Kelvin-Voigt material model consists of the linear spring and viscous damper connected in parallel. In this verification example there is tested the time behaviour of this model during the loading and relaxation in a time interval 24 hours. The constant force Fx is applied for 12 hours and the rest 12 hours is the material model free of load (relaxation). The deformation after 12 and 20 hours is evaluated. Time History Analysis with Linear Implicit Newmark method is used.
Maxwell material model consists of the linear spring and viscous damper connected in series. In this verification example there is tested the time behaviour of this model. The Maxwell material model is loaded by constant force Fx. This force causes initial deformation thanks to the spring, the deformation is then growing in time due to the damper. The deformation is observed at time of loading (20 s) and at the end of the analysis (120 s). Time History Analysis with Linear Implicit Newmark method is used.
In this example, the shear at the interface between concrete cast at different times and the corresponding reinforcement are determined according to DIN EN 1992-1-1. The obtained results with RFEM 6 will be compared to the hand calculation below.
Beam pinned at the both ends is loaded by means the transversal force at the middle. Neglecting its self-weight and shear stiffness, determine the maximum deflection, normal force and moment at the mid-span assuming the second and the third order theory. The verification example is based on the example introduced by Gensichen and Lumpe (see the reference).
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 Z-Section Cantilever is fully fixed at the end and loaded by a torque which, in the case of a shell model, is represented by a couple of shear forces. Determine the axial stress at point A (at mid-surface). The problem is defined according to The Standard NAFEMS Benchmarks.
A cylinder made of elasto-plastic soil is subjected to triaxial test conditions. Neglecting the self-weight, the goal is to determine the limit vertical stress for shear stress failure. An initial hydrostatic stress of 100 kPa is considered.
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 compact disc (CD) rotates at a speed of 10,000 rpm. Therefore, it is subjected to centrifugal force. The problem is modeled as a quarter model. Determine the tangential stress σt on the inner and outer diameters and the radial deflection ur of the outer radius.
A thin plate is fully fixed on the left end and subjected to a uniform pressure. The plate is brought into the elastic-plastic state by the uniform pressure.
A membrane is stretched by means of isotropic prestress between two radii of two concentric cylinders not lying in a plane parallel to the vertical axis. Find the final minimum shape of the membrane - the helicoid - and determine the surface area of the resulting membrane. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in the analytical solution; self-weight is also neglected in this example.
A cylindrical membrane is stretched by means of isotropic prestress. Find the final minimal shape of the membrane - catenoid. Determine the maximum radial deflection of the membrane. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in the analytical solution; self-weight is also neglected in this example.
A spherical balloon membrane is filled with gas with atmospheric pressure and defined volume (these values are used for FE model definition only). Determine the overpressure inside the balloon due to the given isotropic membrane prestress. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in the analytical solution; self-weight is also neglected in this example.
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-walled conical vessel is filled with water. Thus, it is loaded by hydrostatic pressure. While neglecting self-weight, determine the stresses in the surface line and circumferential direction. The analytical solution is based on the theory of thin-walled vessels. This theory was introduced in Verification Example 0084.
A thin-walled spherical vessel is loaded by inner pressure. While neglecting self‑weight, determine the von Mises stress and the radial deflection of the vessel.
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.
A cantilever with a circular cross‑section is loaded by a concentrated bending force and torque. The aim of this verification example is to compare the reduced stress according to the von Mises and Tresca theories.
An open-ended, thick-walled vessel is loaded by inner and outer pressure (therefore, there is no axial stress). While neglecting self-weight, the radial deflection of the inner and the outer radius is determined.
A two-layered, open-ended, thick-walled vessel is loaded by inner and outer pressure; therefore, there is no axial stress. While neglecting self‑weight, the radial deflection of the inner and outer radius, and the pressure (radial stress) in the middle radius is determined.
A compact disc (CD) rotates at a speed of 10,000 rpm. Therefore, it is subjected to centrifugal force. The problem is modeled as a quarter model. Determine the tangential stress on the inner and outer diameters and the radial deflection of the outer radius.
The goal of this example is to demonstrate an irreversible process caused by friction. After the loading and unloading, the end-point is in a different position than where it was at the beginning. Determine the movement of the node in the X direction.
Four columns are fixed at the bottom and connected by a rigid block at the top. The block is loaded by pressure and modeled by an elastic material with a high modulus of elasticity. The outer columns are modeled by linear elastic material and the inner columns by a stress-strain diagram with decaying dependence. Assuming only the small deformation theory and neglecting the structure's self-weight, determine its maximum deflection.
Determine the maximum displacement, in-plane stresses, and stress ratios of a simply supported double-pane glass plate with a foil between both glass panes subjected to uniform pressure.
Determine the maximum deflection and stress in the z-direction of the composite plate, consisting of two glass layers and one foil layer in between, subjected to uniform pressure.
A wide plate with a hole is loaded in one direction by tensile stress. The plate width is large with respect to the hole radius, and it is very thin, considering the state of the plane stress.