A steel beam with a square cross-section is loaded with an axial force and distributed loading. The image shows the calculation of the maximum bending deflection and critical load factor according to the second-order analysis.
A cantilever of rectangular cross‑section has a mass at the end. Furthermore, it is loaded by an axial force. Calculate the natural frequency of the structure. Neglect the self‑weight of the cantilever and consider the influence of the axial force for the stiffness modification.
A cantilever is fully fixed on the left end and loaded by a transverse force and an axial force on the right end. The tensile strength is zero and the behavior in the compression remains elastic.
A cantilever is fully fixed on the left end and loaded by a bending moment on the right end. The material has different plastic strengths under tension and compression.
A thin plate is fully fixed on the left end and loaded by uniform pressure. Plastic material is considered for the calculation.
A structure made of an I-profile is embedded into the fork supports. The axial rotation is restricted on both ends while warping is enabled. The structure is loaded by two transverse forces in the middle. The verification example is based on the example introduced by Gensichen and Lumpe.
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 planar truss consisting of four sloped members and one vertical member is loaded at the upper node by means of a vertical force and an out-of-plane force. Assuming the large deformation analysis and neglecting the self-weight, determine the normal forces of the members and the out-of-plane displacement of the upper node.
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.
A tapered cantilever is fully fixed on the left end and loaded by a continuous load. Plastic material is considered for the calculation.
A thin plate is fully fixed on the left end and loaded by uniform pressure on the top surface.
Using AISC Manual tables, determine the available compressive and flexural strengths and whether the ASTM A992 W14x99 beam has sufficient available strength to support the axial forces and moments shown in Figure 1, obtained from a second-order analysis that includes P-𝛿 effects.
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 thin plate is fully fixed on the left end and loaded by uniform pressure on the top surface. Determine the maximum deflection. The aim of this example is to show that a surface of the surface stiffness type Without Membrane Tension behaves linearly under bending.
Continuous beam with four spans is loaded by axial and bending forces (replacing imperfections). All supports are fork - warping is free. Determine displacements uy and uz, moments My, Mz, Mω and MTpri and rotation φx. The verification example is based on the example introduced by Gensichen and Lumpe.
A structure made of I-profile trusses is supported on the both ends by the spring sliding supports and loaded by the transversal forces. The self-we ight is neglected in this example . Determine the deflection of the structure, the bending moment, the normal force in given test points and horizontal deflection of the spring support.
A structure made of an I-profile is fully fixed on the left end and embedded into the sliding support on the right end. The structure consists of two segments. The self-weight is neglected in this example. Determine the maximum deflection of the structure, the bending moment on the fixed end, the rotation of segment 2, and the reaction force at point B by means of the geometrically linear analysis and the second-order analysis. The verification example is based on the example introduced by Gensichen and Lumpe.
A cantilever is fully fixed on the left end and loaded by a bending moment. Plastic material is considered for the calculation.
The axial rotation of the I-profile is restricted on the both ends by means of the fork supports (warping is not restricted). The structure is loaded by two transverse forces in its middle. The self-weight is neglected in this example. Determine the maximum deflections of the structure uy,max and uz,max, maximum rotation φx,max, maximum bending moments My,max and Mz,max and maximum torsional moments MT,max, MTpri,max, MTsec,max and Mω,max. The verification example is based on the example introduced by Gensichen and Lumpe.
Using AISC Manual tables, determine the available compressive and flexural strengths and whether the ASTM A992 W14x99 beam has sufficient available strength to support the axial forces and moments shown in Figure 1, obtained from a second-order analysis that includes P-𝛿 effects.
A console is loaded by concentrated force at its free end. Determine the maximum deflection of the console using large deformation analysis.
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).
A cantilever from a rectangular cross-section is lying on an elastic Pasternak foundation and loaded by distributed loading. The image shows the calculation of the maximum deflection and maximum bending moment.
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 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 structure made of I-profile is fully fixed on the left end and embedded into the sliding support on the right end. The structure consists of two segments. The self-weight is neglected in this example. Determine the maximum deflection of the structure uz,max, the bending moment My on the fixed end, the rotation &svarphi;2,y of the segment 2 and the reaction force RBz by means of the geometrically linear analysis and the second-order analysis. The verification example is based on the example introduced by Gensichen and Lumpe.
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 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.
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.
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.