To do this, an initial position for this reference location can be found by setting Equation 2 and 3 equal. A convenient way of calcuating the nominal stress at the area with a hole is done by computing the stress at another location on the beam where there is no discontinuity. It should be noted that Equations 2 and 3 are only valid for a rectangular beam with a point load. The nominal stress refers to the stress based on the net area of the section.ġ.2.Mathematical Derivation for Equations UsedAs proven in previous experiments, the value for stress can be calculated with the following formula.Įquation 2 P is the magnitude of the force applied L is the longitudinal length from the clamp to the load x is the longitudinal distance from the clamp to the cross sectional area being inspectedī is the base dimension of the beam t is the thickness of the beam The nominal stress for a cross sectional area with a hole can be expressed as:Įquation 3 where d is the diameter of the hole. Kt =Įquation 1 For a hole, the maximum stress is always found at the closest position to the discontinuity because this is where the material has the least amount of support. The stress concentration factor is a ratio of two stresses, as shown below. A standard means of computing the maximum theoretical stress around a irregularity is found in the stress concentration factor, Kt. Extensive research into the effects of these discontinuities, called "stress-risers" has been conducted previously. A simple irregularity, a drilled hole, is studied within this experiment such that the effects of this feature can be analyzed and explored. Introduction & Background1.1.General BackgroundGeometric irregularities on loaded members can dramatically change stresses in the structure. Mathematical Derivation for Equations Used.4 2. The stress concentration factor for Aluminum 2024-T6 was ultimately found to be approximately 1.485. As a second opinion, ANSYS was used to verify and visually render the stress concentrations over the surface of the beam.
This resulting stress profile was measured, as well as theoretically determined with Statics.
When a load is applied to the unsupported end of the beam, the stress adjacent to the hole increases dramatically more than the area closest to the edge. The following exercise explores the effect of a hole in an otherwise uniform rectangular aluminum cantilever beam. The stress concentration, expressed as the maximum stress under loading divided by the nominal stress, can mathematically predict the maximum stress for different nominal loadings.
Mechanics of Materials Laboratory Cantilever Flexure Testĭavid Clark Group C:David Clark Jacob Parton Zachary Tyler Andrew SmithĪbstractStress risers, geometric irregularities that break the uniformity of a material, cause a predictable increase in stress.