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AFGROW | DTD Handbook

Handbook for Damage Tolerant Design

  • DTDHandbook
    • About
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    • Sections
      • 1. Introduction
      • 2. Fundamentals of Damage Tolerance
      • 3. Damage Size Characterizations
      • 4. Residual Strength
        • 0. Residual Strength
        • 1. Introduction
        • 2. Failure Criteria
        • 3. Residual Strength Capability
        • 4. Single Load Path Structure
        • 5. Built-Up Structures
          • 0. Built-Up Structures
          • 1. Edge Stiffened Panel with a Central Crack
          • 2. Centrally and Edge Stiffened Panel with a Central Crack
          • 3. Analytical Methods
          • 4. Stiffener Failure
          • 5. Fastener Failure
          • 6. Methodology Basis for Stiffened Panel Example Problem
          • 7. Tearing Failure Analysis
          • 8. Summary
        • 6. References
      • 5. Analysis Of Damage Growth
      • 6. Examples of Damage Tolerant Analyses
      • 7. Damage Tolerance Testing
      • 8. Force Management and Sustainment Engineering
      • 9. Structural Repairs
      • 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
      • 11. Summary of Stress Intensity Factor Information
    • Examples

Section 4.5.4. Stiffener Failure

Stiffener failures are based on the following three stiffener conditions:

1.      Intact stiffener (no cracks),

2.      Partially failed stiffener (with cracks),

3.      Totally failed stiffener.

The failure criterion for the intact stiffener is based on the ultimate strength criterion.  As mentioned earlier, the ratio between the stiffener load in the cracked region (Pmax) and the remote region from the crack (P) is defined as the load concentration factor Ls or


where s is the uniform stress in the skin at the loaded end of the panel and As is the stiffener cross sectional area.  Failure of the stiffener will occur when the value of Pmax is equal to the ultimate strength of the stiffener (Pult), or when

Pmax = Pult = y sult As


where sult is the ultimate tensile strength of the stiffener material and y < 1 is a factor accounting for load eccentricity and notch effects in the stiffener.  For a uniform stress distribution in the panel remote from the crack the stress in the stringer will equal the nominal stress s in the skin, i.e.,

P = sAs



Combining equations 4.5.1 to 4.5.2, yields the following stiffener failure criterion:


When the stress in the stringer reaches the value of y sult, the stringer will fail.  The parameter y is determined by tests.

When load eccentricity and not effects are not considered for a stringer, y equals one.  The stiffener failure curve obtained using Equation 4.5.4 is shown in Figure 4.5.11.  The initial portion of the residual strength curve is flat because the load concentration factor Ls is equal to one for small skin crack lengths.  As the skin crack increases in size, Ls becomes significantly greater than one and the stringer carries a large portion of the total structural load which eventually leads to stringer yielding and failure.  The portion of the curve in Figure 4.5.11 corresponding to Ls > 1 shows the gradual reduction of the residual strength.

Figure 4.5.11.  Residual Strength Diagram for Stiffener

When the load eccentricity and notch effects in the stiffener are considered, the parameter y in Equation 4.5.4 is less than one.  The residual strength corresponding to a case where y < 1 is shown in Figure 4.5.11.  The curve CD does not have the initial flaw portion exhibited by the case y = 1.  Instead, the residual strength starts decreasing even for small skin crack lengths.  The residual strength diagram for the stringer can be constructed knowing the values of Ls and y.  Determining Ls requires numerical solution techniques that are discussed in the example presented in subsection 4.5.7.

According to JSSG-2006 requirements, cracks are assumed in all load carrying members.  This means that all structural elements, stringer included, are assumed to be damaged.  The residual strength diagram for the stringer will involve using the fracture mechanics approach of predicting unstable crack growth.  The critical stress for a partially cracked stringer is given by  where Kcr is the appropriate fracture toughness, bs is the stringer geometric parameter, and as is the stringer crack size.  When the crack in the panel approaches the stringer, the load transmitted to the stringer will become large (Ls >> 1) and thus the critical stress level required to fail the stringer rapidly decreases as shown by curve CE in Figure 4.5.11.  Curve CE corresponds to the total failure of the stringer.  This may happen when a large crack emanates from a stringer rivet hole.  Total failure of the stiffener occurs before the skin crack approaches the stiffeners.

The residual strength diagram for the stiffened panel in this case would, in fact, be approximately that of the unstiffened panel.

The foregoing discussion presented analysis of a riveted built-up structure.  However, built-up structures exist in which the stringer is adhesively bonded to the skin.  The load transfer from the skin to the stringer is more effective in the bonded structure due to the increased rigidity in the stiffener.  The corresponding load transfer parameter Ls will have higher values as shown schematically in Figure 4.5.12a.  Due to the effective load transfer from the skin to the stiffener, the applied stress-intensity factor will be reduced when the panel crack approaches the stiffener.  Figure 4.5.12b illustrates the levels of stress-intensity factor that occur for riveted and bonded stiffeners.  The figure also shows that the bonded stiffener is subjected to higher loads due to the effective load transfer; the higher load causes the stiffener failure of the bonded structure to be more critical than that of the riveted structure.  Figure 4.5.13 compares the decay of residual strength for these two types of structures.  The residual strength of the bonded stiffener decreases faster than the riveted stiffener.  In the determination of the residual strength diagram, the parameter Ls is usually calculated by numerical methods.  The steps to obtain Ls are discussed later in this section.

Figure 4.5.12.  Comparison of Ls and K/s for Riveted and Bonded Structures

Figure 4.5.13.  Comparison of Residual Strength for Riveted and Bonded Stiffeners