A reinforced concrete beam is designed as a two-span beam with a cantilever. The cross-section varies along the length of the cantilever (tapered cross-section). The internal forces, the required longitudinal and shear reinforcement for the ultimate limit state are calculated.
Consider an ASTM A992 W 18x50 beam forspan and uniform dead and live loads as shown in Figure 1. The member is limited to a maximum nominal depth of 18 inches. The live load deflection is limited to L/360. The beam is simply supported and continuously braced. Verify the available flexural strength of the selected beam, based on LRFD and ASD.
The goal of this verification example is to analyze the fluid flow around the glider. The task is to determine the drag coefficient and the lift coefficient with respect to the angle of attack. These coefficients can also be drawn into the graph of the drag polar. The limit angle for laminar fluid flow around the wing profile can also be determined from the velocity field. The available 3D CAD model (STL file) is used in RWIND 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 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 symmetrical shallow structure is made of eight equal truss members, which are embedded into hinge supports. The structure is loaded by a concentrated force and alternatively by imposed nodal deformation over the critical limit point when the snap-through occurs. Imposed nodal deformation is used in RFEM 5 and RSTAB 8 to obtain the full equilibrium path of the snap-through. The self-weight is neglected in this example. Determine the relationship between the actual loading force and the deflection, considering large deformation analysis. Evaluate the load factor at the given deflections.
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 structure is made of four truss members, which are embedded into hinge supports. The structure is loaded by a concentrated force and alternatively by imposed nodal deformation over the critical limit point, when snap-through occurs. Imposed nodal deformation is used in RFEM 5 and RSTAB 8 to obtain the full equilibrium path of the snap-through. The self-weight is neglected in this example. Determine the relationship between the actual loading force and the deflection, considering large deformation analysis. Evaluate the load factor at given deflections.
Consider an ASTM A992 W 18×50 beam forspan and uniform dead and live loads as shown in Figure 1. The member is limited to a maximum nominal depth of 18 inches. The live load deflection is limited to L/360. The beam is simply supported and continuously braced. Verify the available flexural strength of the selected beam, based on LRFD and ASD.
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 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.
Consider a rigid scaffolding tube, fixed at the bottom using the Scaffolding Nodal Support and loaded by both a moment and a force. Calculate the maximum radial deflection by exceeding the capacity of the scaffolding support.
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.