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.
Verify that a beam of different cross-sections made of Alloy 6061-T6 is adequate for the required load, in accordance with the 2020 Aluminum Design Manual.
Determine the allowable axial compressive strength of a pinned 8-foot-long beam of various cross-sections made of Alloy 6061-T6 and laterally restrained to prevent buckling about its weak axis in accordance with the 2020 Aluminum Design Manual.
Determine the first sixteen natural frequencies of a double cross with a square cross-section. Each of the eight arms is modeled by means of four beam elements and has a pin support at the end (the x- and y-deflections are restricted). The vibrations are considered only in plane xy. The problem is defined according to The Standard NAFEMS Benchmarks.
Determine the allowable axial compressive strength of a pinned 8-foot-long beam of various cross-sections made of Alloy 6061-T6 and laterally restrained to prevent buckling about its weak axis in accordance with the 2020 Aluminum Design Manual.
Verify that a beam of different cross-sections made of Alloy 6061-T6 is adequate for the required load, in accordance with the 2020 Aluminum Design Manual.
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.
Determine the allowable axial compressive strength of a pinned 8-foot-long beam of various cross-sections made of Alloy 6061-T6 and laterally restrained to prevent buckling about its weak axis in accordance with the 2015 Aluminum Design Manual.
Verify that a beam of different cross-sections made of Alloy 6061-T6 is adequate for the required load, in accordance with the 2015 Aluminum Design Manual.
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.
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.
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 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 rod with a square cross-section is fixed on the top end. The rod is loaded by self-weight. For comparison, the example is also modeled with the concentrated force load, the value of which is equal to the gravity. The aim of this verification example is to show the difference between these types of loading, although the total loading force is equal.
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 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.
A cantilever beam with an I-beam cross-section of length L is defined. The beam has five mass points with masses m acting in the X-direction. The self-weight is neglected. The frequencies, mode shapes, and equivalent loads of this 5-DOF system are analytically calculated and compared with the results from RSTAB and RFEM.
Determine the torsional constant for the cross-section of the tube (annular area) analytically, and compare the results with the numerical solution in RFEM 5 and RSTAB 8 for various wall thicknesses.
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.
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.
An axially loaded steel beam with a square cross-section is pinned at one end and spring-supported at the other. Two cases with different spring stiffnesses are considered. The verification example solves the calculation of the load factors of the beam in the image using the linear stability analysis.
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.