One layered square orthotropic plate is fully fixed at its middle point and subjected to pressure. Compare the deflections of the plate corners to check the correctness of the transformation.
Prove that coupling different dimensional elements does not affect the results. A cantilever with a rectangular cross-section is fixed at one end and loaded at the other by concentrated forces. Neglecting its self-weight and assuming only small deformations, determine the cantilever's maximum deflections.
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.
A steel cable or membrane with pins on both ends is loaded by distributed loading. Neglecting its self-weight, determine the maximum deflection of the structure using the large deformation analysis.
A vertical cantilever with a square cross-section is loaded at the top by tensile pressure. The cantilever consists of an isotropic material. Calculate the deflection.
Determine the bending moment which, acting at the free end of the cantilever, will bend the member into a circular shape. Neglecting the beam's self-weight, assuming the large deformation analysis, and loading the cantilever with the moment, determine its maximum deflections.
A structure is made of two trusses, which are embedded into the hinge supports. The structure is loaded by concentrated force. The self-weight is neglected. Determine the relationship between the loading force and the deflection, considering large deformations.
A structure made of I-profile trusses is supported on both ends by spring sliding supports and loaded by transversal forces. The self-weight is neglected in this example. Determine the deflection of the structure, the bending moment, the normal force in the given test points, and the horizontal deflection of the spring supports.
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.
An I-profile cantilever is supported on the left end and loaded by torque. The aim of this example is to compare the fixed support with the fork support and to investigate the behavior of some representative quantities. Comparison is also made to the solution by means of plates. Small deformations are considered, and the self-weight is neglected. Determine the rotation in the midpoint of the cantilever, and in case of the member entity with warping, determine the values of the primary torsional moment, the secondary torsional moment, and the warping moment both on the left end (point A) and the right end (point B).
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.
A slightly sloped member is loaded by concentrated force, held by a spring at one end, and supported at the other end. Assuming large deformations and neglecting the member's self-weight, determine its maximum upward deflection.
A structure is made of two trusses of unequal length, which are embedded into the hinge supports. The structure is loaded by concentrated force. The self-weight is neglected. Determine the relationship between the loading force and the deflection, considering large deformations.
A thin-walled cantilever of a QRO-profile is fully fixed on the left end and warping is enabled. The cantilever is subjected to torque. Small deformations are considered, and the self-weight is neglected. Determine the maximum rotation, primary moment, secondary moment, and warping moment. The verification example is based on the example introduced by Gensichen and Lumpe.
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 member with the given boundary conditions is loaded by torsional moment and axial force. Neglecting its self-weight, determine the beam's maximum torsional deformation as well as its inner torsional moment, defined as the sum of a primary torsional moment and torsional moment caused by the normal force. Provide a comparison of those values while assuming or neglecting the influence of the normal force. The verification example is based on the example introduced by Gensichen and Lumpe.
Time history analysis of a cantilever beam (SDOF system) excited by a periodic function. Vertical deformations and accelerations calculated with direct integration and modal analysis in RF‑/DYNAM Pro - Forced Vibrations are compared with the analytical solution.
A simply supported rectangular Kirchhoff plate is subjected to both uniform lateral pressure and stretched by a distributed load. The maximum out-of-plane deflection is determined by assuming small deformations.
An elliptic plate with a clamped boundary is subjected to a uniformly distributed transverse load. Assuming the small deformation theory and neglecting the self‑weight, the maximum out‑of‑plane deflection of the plate is determined.
A simply supported equilateral triangular plate is subjected to a uniformly distributed transverse load. Assuming the small deformation theory and neglecting self‑weight, the maximum out‑of‑plane deflection of the plate is determined.
A simply supported rectangular plate is subjected to different load types. Assuming only the small deformation theory and neglecting self-weight, determine the deflection at its centroid for each load type.
A concentrated force is suddenly applied at the mid‑span of a simply supported beam at a given time. Considering only the small deformation theory, determine the maximum deflection of the beam.
A concentrated force is applied for a short period of time at the mid‑span of a simply supported beam. Considering only the small deformation theory and assuming that the mass of the beam is concentrated at its mid‑span, determine its maximum deflection.
A steel rod between two rigid supports with a gap is loaded by a temperature difference. While neglecting self‑weight, determine the total deformation of the rod and its internal axial force.
A pinned beam with a rectangular cross‑section is subjected to distributed loading and shifted vertically by eccentricity. Considering the small deformation theory, neglecting the self‑weight, and assuming that the beam is made of isotropic elastic material, determine the maximum deflection.
The mathematical pendulum consists of a zero‑weight rope and a mass point at its end. The pendulum is initially deflected. Determine the angle of the rope at the given test time.
A very stiff cable is suspended between two supports. Determine the equilibrium shape of the cable (the catenary), consider the gravitational acceleration, and neglect the stiffness of the cable. Verify the position of the cable at the given test points.