A timber beam reinforced by two steel plates at the ends is loaded by pressure. The wood fibers are parallel to the upper loaded side of the beam. Plastická plocha je popsána podle teorie plasticity Tsai-Wu.
Konzola je plně fixována na levém konci a zatížena příčnou silou a normálovou silou na pravém konci. The tensile strength is zero and the behavior in the compression remains elastic.
Dokažte, že spojení různých rozměrových prvků nemá vliv na výsledky. 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.
A timber beam reinforced by two steel plates at the ends is loaded by pressure. The wood fibers are parallel to the upper loaded side of the beam. Plastická plocha je popsána podle teorie plasticity Tsai-Wu.
Konstrukce se skládá ze dvou nosníků, které jsou uloženy na kloubových podporách. 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. Vlastní tíha se v tomto příkladu nezohledňuje. 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.
Nosník je na levém konci zcela upevněn (deplanace je omezena) a na pravém konci je podepřen vidlicovou podporou (deplanace je povolena). The beam is subjected to a torque, longitudinal force, and transverse force. Determine the behavior of the primary torsional moment, secondary torsional moment, and warping moment. The verification example is based on the example introduced by Gensichen and Lumpe.
Nosník uložený na obou koncích je zatížen soustředěnou silou uprostřed. 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.
Konstrukce se skládá ze dvou nosníků různé délky, které jsou uloženy na kloubových podporách. 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 an I-profile is fully fixed on the left end and embedded into the sliding support on the right end. Konstrukce se skládá ze dvou segmentů. 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 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. Tyto hodnoty porovnáme při zohlednění nebo zanedbání vlivu normálové síly. The verification example is based on the example introduced by Gensichen and Lumpe.
A long, thin beam is carrying a concentrated mass and is loaded by a time-dependent force. Je prostě podepřený. The problem is described using the following parameters. Determine the deflections in the given test times.
Časová analýza konzoly (SDOF - systém s jedním stupněm volnosti), která je buzena periodickou funkcí. Vertical deformations and accelerations calculated with direct integration and modal analysis in RF‑/DYNAM Pro - Forced Vibrations are compared with the analytical solution.
Tento příklad slouží jako ukázka vazby diafragma. The application is shown on a two-story structure. The structure is loaded by means of lateral forces according to Figure 1. Determine the maximum deflection of the structure ux in the direction of the loading forces using both the diaphragm constraint and the plate model of the floor.
Tyč se čtvercovým průřezem je na svém horním konci vetknutá. 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.
Dvoupodlažní rámová konstrukce o jednom poli je vystavena seizmickému zatížení. The modulus of elasticity and cross‑section of the frame beams are much larger than those of the columns, so the beams can be considered rigid. The elastic response spectrum is given by the standard SIA 261/1:2003. Neglecting self-weight and assuming the lumped masses are at the floor levels, determine the natural frequencies of the structure. For each frequency obtained, specify the standardized displacements of the floors as well as equivalent forces generated using the elastic response spectrum according to the standard SIA 261/1.2003.
A truss structure consists of three rods (one steel and two copper) joined by a rigid member. The structure is loaded by a concentrated force and a temperature difference. Celkový průhyb konstrukce je stanoven bez zohlednění vlastní tíhy.
Ocelový prut mezi dvěma tuhými podporami se spárou na jednom konci je zatížen rozdílem teplot. While neglecting self‑weight, determine the total deformation of the rod and its internal axial force.
A cantilever of rectangular cross‑section has a mass at the end. Kromě toho je zatížena normálovou silou. 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.
Jednoduchý oscilátor se skládá z tělesa o hmotnosti m (uvažuje se pouze ve směru osy x) a lineární pružiny s tuhostí k . The mass is embedded on a surface with Coulomb friction and is loaded by constant-in-time axial and transverse forces.
A closely coiled helical spring is loaded by a compression force. The spring has middle diameter D, wire diameter d, and it consists of i turns. Celková délka pružiny je L. Determine the total deflection of the spring for the member model and one‑turn deflection for the solid model.
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. Stanovíme celkový průhyb zakřiveného nosníku bez zohlednění vlastní tíhy.
Tlumený jednohmotový systém je zatížen konstantní silou. Determine the spring force, damping force, and inertial force at the given test time. In this verification example, the Kelvin--Voigt dashpot (namely, a spring and a damper element in serial connection) is decomposed into its purely viscous and purely elastic parts, in order to better evaluate the reaction forces.
Konstrukce se skládá ze čtyř prutů, které jsou uloženy na kloubových podporách. 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.
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. Vlastní tíha se v tomto příkladu nezohledňuje. Determine the relationship between the actual loading force and the deflection, considering large deformation analysis. Evaluate the load factor at the given deflections.
A cable is loaded by means of a uniform load. Výsledkem je deformovaný tvar kruhového segmentu. Determine the equilibrium force of the cable to obtain the given sag of the cable. 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.
Tento verifikační příklad vychází z verifikačního příkladu 0122. A single-mass system without damping is subjected to an axial loading force. An ideal elastic-plastic material with characteristics is assumed. Determine the time course of the end-point deflection, velocity, and acceleration.
A sphere is subjected to a uniform flow of viscous fluid. The velocity of the fluid is considered at infinity. The goal is to determine the drag force. The parameters of the problem are set so that the Reynolds number is small and the radius of the sphere is also small, thus the theoretical solution can be reached - Stokes flow (G. G. Stokes 1851).
Rovinný příhradový vazník, který se skládá ze čtyř šikmých prutů a jednoho svislého prutu, je zatížen v horním uzlu svislou silou a silou mimo rovinu. 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.