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 (P_max) and the remote region from the crack (P) is defined as the load concentration factor L_s or

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

where s_ult 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.,

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 s_ult, 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 L_s is equal to one for small skin crack lengths.  As the skin crack increases in size, L_s 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 L_s > 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 L_s and y.  Determining L_s 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 K_cr is the appropriate fracture toughness, b_s is the stringer geometric parameter, and a_s is the stringer crack size.  When the crack in the panel approaches the stringer, the load transmitted to the stringer will become large (L_s >> 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 L_s 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 L_s is usually calculated by numerical methods.  The steps to obtain L_s 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