The following table contains the formulas describing the static response of the cantilever beam under a concentrated point force.The tool calculates and plots diagrams for these quantities: reactions bending moments transverse shear forces deflections slopes Please take in mind that the assumptions of Euler-Bernoulli beam theory are adopted, the material is elastic and the cross section is constant over the entire beam span (prismatic beam).Jump to the theory and formulas instead Units: Imperial Metric 1 2 3 4 Structure L m cm mm yd ft in Optional properties, required only for deflectionslope results: E Pa kPa MPa GPa psi ksi Mpsi I m4 cm4 mm4 ft4 in4 Calculate the moment of inertia of various beam cross-sections, using our dedicated calculators.
ADVERTISEMENT 1 2 3 4 Imposed loading: Uniform distributed load Uniform distr. The support is a, so called, fixed support that inhibits all movement, including vertical or horizontal displacements as well as any rotations. Lifting Beam Design Calculations Free To MoveThe other end is unsupported, and therefore it is free to move or rotate. The cantilever features only a single fixed support Removing the singe support or inserting an internal hinge, would render the cantilever beam into a mechanism: a body the moves without restriction in one or more directions. As a result, the cantilever beam offers no redundancy in terms of supports. If a local failure occurs the whole structure would collapse. These type of structures, that offer no redundancy, are called critical or determinant structures. To the contrary, a structure that features more supports than required to restrict its free movements is called redundant or indeterminate structure. ADVERTISEMENT Assumptions The static analysis of any load carrying structure involves the estimation of its internal forces and moments, as well as its deflections. Typically, for a plane structure, with in plane loading, the internal actions of interest are the axial force. The calculated results in this page are based on the following assumptions: The material is homogeneous and isotropic (in other words its characteristics are the same in ever point and towards any direction) The material is linear elastic The loads are applied in a static manner (they do not change with time) The cross section is the same throughout the beam length The deflections are small Every cross-section that initially is plane and also normal to the longitudinal axis, remains plane and normal to the deflected axis too. ![]() The last two assumptions satisfy the kinematic requirements for the Euler Bernoulli beam theory that is adopted here too. ![]() The following are adopted here: The axial force is considered positive when it causes tension to the part The shear force is positive when it causes a clock-wise rotation of the part. The bending moment is positive when it causes tension to the lower fiber of the beam and compression to the top fiber. A different set of rules, if followed consistently would also produce the same physical results. Positive sign convention for internal axial force, N, shear force, V, and bending moment, M Symbols. The following table contains the formulas describing the static response of the cantilever beam under a uniform distributed load. In practice however, the force may be spread over a small area, although the dimensions of this area should be substantially smaller than the cantilever length. In the close vicinity of the force application, stress concentrations are expected and as result the response predicted by the classical beam theory is maybe inaccurate. As we move away from the force location, the results become valid, by virtue of the Saint-Venant principle.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |