Search results
Results from the WOW.Com Content Network
The K-factor is the bending capacity of sheet metal, and by extension the forumulae used to calculate this. [1] [2] [3] Mathematically it is an engineering aspect of geometry. [4] Such is its intricacy in precision sheet metal bending [5] (with press brakes in particular) that its proper application in engineering has been termed an art. [4] [5]
, unsupported length of column,, column effective length factor; This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] The column will remain straight for loads less than the critical load. The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load ...
where K is the stress intensity factor (with units of stress × length 1/2) and is a dimensionless quantity that varies with the load and geometry. Theoretically, as r goes to 0, the stress σ i j {\displaystyle \sigma _{ij}} goes to ∞ {\displaystyle \infty } resulting in a stress singularity. [ 5 ]
The K-factor formula does not take the forming stresses into account but is simply a geometric calculation of the location of the neutral line after the forces are applied and is thus the roll-up of all the unknown (error) factors for a given setup. The K-factor depends on many variables including the material, the type of bending operation ...
The other method, namely the secant method, uses the compliance-crack length equation given by ASTM standard to calculate effective crack length from an effective compliance. Compliance at any point in Load vs displacement curve is essentially the reciprocal of the slope of the curve that ensues if the specimen is unloaded at that point.
A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of a fatigue crack can result in catastrophic failure, particularly in the case of aircraft. When many growing fatigue cracks interact with one another it is known as widespread fatigue damage. A crack growth equation can be used to ...
It is a function of the Young's modulus, the second moment of area of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending stiffness of a beam can analytically be derived from the equation of beam deflection when it is applied by a force.
The system stiffness matrix K is square since the vectors R and r have the same size. In addition, it is symmetric because k m {\displaystyle \mathbf {k} ^{m}} is symmetric. Once the supports' constraints are accounted for in (2), the nodal displacements are found by solving the system of linear equations (2), symbolically: