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Stress concentration occurs at points of discontinuity such as holes or abrupt changes in cross-section within a structural member. These geometric irregularities create localized regions where stress amplifies significantly above the average stress level. The severity of stress concentration depends only on the ratios of geometric parameters, not on the member's size or material type.

The stress concentration factor is defined as the ratio of maximum stress to average stress in the critical section at a discontinuity. Engineers compute this factor from geometric ratios and multiply it by the average stress to determine maximum stress under given axial loads. This method is valid only when maximum stress remains below the material's proportional limit.

Stress distribution in members with discontinuities is governed purely by geometric parameters such as hole radius or fillet dimensions relative to cross-sectional widths. Material properties do not influence how stress concentrates at these points. This geometric independence allows engineers to use universal stress concentration factors across different materials and member sizes.

The photoelastic method is used experimentally to determine stress distribution in structural members with discontinuities like circular holes or fillets. This technique visualizes stress patterns based on geometric ratios and validates theoretical stress concentration factors. Results from photoelastic analysis help engineers predict maximum stress locations under deformation of member under multiple loadings.

Stress concentration factors are valid only when maximum stress does not exceed the material's proportional limit, the threshold where stress and strain maintain a linear relationship. Beyond this limit, the linear assumptions underlying stress concentration factor calculations break down. Engineers must verify that calculated maximum stresses remain within this elastic range for accurate design predictions.

Both fillets and circular holes create stress concentrations, but their effects depend on different geometric ratios. Circular holes involve the ratio of hole radius to smaller width, while fillets depend on ratios of hole radius to smaller width and larger width to smaller width. Both discontinuities amplify localized stress, requiring engineers to apply appropriate stress concentration factors during structural design.

Calculating exact stress distributions is complex and often unnecessary for design purposes. Instead, engineers use stress concentration factors to ensure maximum stress in a critical section does not exceed allowable stress under specific loads. This practical approach simplifies structural design while maintaining safety by focusing on the most critical stress points near discontinuities.