Cantilever beam is a kind of cantilever beam obtained in material mechanics to facilitate calculation and analysissimplified model , one end of the cantilever beam isFixed supportAnd the other end is the free end.Under the load, the support reaction at the fixed end of the cantilever beam can be obtained according to the force balance condition, including the horizontal force, vertical force and bending moment, and the axial diagram, shear diagram and bending moment diagram can be drawn accordingly.Since the beam generally bears the action of vertical concentrated load or uniform load, the horizontal reaction force of the support is 0.
Simply supported beam, cantilever beam andOutriggerThey are three basic forms of statically determinate beams commonly seen in engineering.In practical engineering, the force of beam and the constraint of support are complex.In order to facilitate analysis and calculation, it is necessary to simplify the actual structure, including the structure, support and load of the beam. For example, the cantilever beam can be simplified into a cantilever beam model, from which the calculation diagram of the beam can be obtained.
Because the cantilever beam is a statically determinate structure, the temperature change of the system, concrete shrinkage and creep, support movement, etc. will only make the cantilever beam deformed, but will not produce additional internal forces in the cantilever beam.
design requirement
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When estimating the section size, the section height of the concrete cantilever beam is generally 1/5 of the cantilever length.
Position of starting point of rebar bending[1]
When calculating the reinforcement, there should be no less than 2 upper reinforcements extending to the outer end of the cantilever beam and bending down for no less than 12d. The rest of the reinforcements should not be cut off at the upper part of the beam, but should be bent down at the starting point of the bending specified in the specification, and anchored at the lower side of the beam as specified.The bending angle should be 45 ° or 60 °. The anchorage length parallel to the beam axis direction should be reserved outside the bending end point, and it should not be less than 20d in the tension zone and 10d in the compression zone.As shown in the figure "Position of starting point of rebar bending".
Calculate deflection
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In material mechanicsSmall deformation hypothesisOn the premise that the deflection at any section of the cantilever beam can be obtained by superposition principle according to the deflection at the free end, or by integral solution using the method in structural mechanics. When one of the influence line bending moment diagram or the actual load bending moment diagram is a straight line, it can also be directly usedGraph multiplicationSolve the deflection.The following table shows the deflection calculation formula of cantilever beam under different loads.
Bending moment diagram and maximum deflection of cantilever beam under different loads (I)
Bending moment diagram and maximum deflection of cantilever beam under different loads (II)
