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.
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.
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.
The model is based on the example 4 of [1]: Point-supported slab.
The flat slab of an office building with crack-sensitive lightweight walls is to be designed. Inner, border and corner panels are to be investigated. The columns and the flat slab are monolithically joined. The edge and corner columns are placed flush with the edge of the slab. The axes of the columns form a square grid. It is a rigid system (building stiffened with shear walls).
The office building has 5 floors with a floor height of 3.000 m. The environmental conditions to be assumed are defined as "closed interior spaces". There are predominantly static actions.
The focus of this example is to determine the slab moments and the required reinforcement above the columns under full load.
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 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 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 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.
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 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.
An inner column in the first floor of a three-story building is designed. The column is monolithic connected with the top and bottom beams. The fire design simplified method A for columns according to EC2-1-2 is than proofed and the results compared to [1].
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 reinforced concrete column is designed for ULS at normal temperature according to DIN EN 1992-1-1/NA/A1:2015, based on 1990-1-1/NA/A1:2012-08. The design employs the nominal curvature method; see DIN EN 1992-1-1, Section 5.8.8. The addressed column is located at the edge of a 3-span frame structure, which consists of 4 cantilever columns and 3 individual trusses hinged to them. The column is subjected to the vertical force of the precast truss, snow and wind. The results are compared with the literature.
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.
In this verification example, the capacity design values of shear forces on beams are calculated in accordance with EN 1998-1, 5.4.2.2 and 5.5.2.1 as well as the capacity design values of columns in flexure in accordance with 5.2.3.3(2). The system consists of a two span reinforced concrete beam with a span length of 5.50m. The beam is part of a frame system. The results obtained are compared with those in [1].
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.
This verification example compares wind load calculations on a flat roof building using the ASCE 7-16 standard and using CFD simulation in RWIND Simulation. The building is defined according to the sketch and the inflow velocity profile taken from the ASCE 7-16 standard.
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.
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.
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.
A reinforced concrete slab inside a building is to be designed as a 1.0 m stripe with members. The floor slab is uniaxially spanned and runs through two spans. The slab is fixed on masonry walls with free-rotating supports. The middle support has a width of 240 mm and the two edge supports have a width of 120 mm. The two spans are subjected to an imposed load of category C: congregation areas.
An ASTM A992 14×132 W-shaped column is loaded with the given axial compression forces. The column is pinned top and bottom in both axes. Determine whether the column is adequate to support the loading shown in Figure 1 based on LRFD and ASD.
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.
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.
An ASTM A992 W 24×62 beam with end shears of 48.000 and 145.000 kips from the dead and live loads, respectively, is shown in Figure 1. Verify the available shear strength of the selected beam, based on LRFD and ASD.
Determine the required strengths and effective length factors for the ASTM A992 material columns in the moment frame shown in Figure 1 for the maximum gravity load combination, using LRFD and ASD.
An ASTM A992 W-shaped member is selected to carry a dead load of 30.000 kips and a live load of 90.000 kips in tension. Verify the member strength using both LRFD and ASD.
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 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.
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.