## 4 Results and Discussions
### Ultimate Compressive Strength of Cracked Stiffened Panels  
Figure 9 and Table 4 compare the ultimate strength of stiffened panels with perpendicular cracks under uniaxial compression, as calculated by Equation (5). The existing formula underestimates the strength of these stiffened panels because it assumes a uniformly reduced cross-sectional area, neglecting the load redistribution effect provided by the stiffening elements. For longitudinal strength with a transverse crack, the results of this study showed little deviation from the equation, as the cracked area was relatively small compared to the original cross-section, and its impact on the overall structure was minimal. However, a significant gap appears when the structure is subjected to transverse compression with longitudinal cracks. Equation (5) assumes a uniformly reduced cross-sectional area based on the ratio of the cracked area to the total area. This leads to an underestimation, as it applies the original strength without considering the fact that, at the ultimate limit state, most of the load is carried by the edges. These edges are where the stiffening elements are concentrated (see Figure A20). Figures 10 and 11 compare the structural response of intact and cracked stiffened panels under longitudinal and transverse uniaxial compression, while Figure 12 illustrates the ultimate compressive strength of the panels under both uniaxial and biaxial compressions. The influence of longitudinal and transverse cracks on the ultimate strength of stiffened panels was less significant compared to that of plates. This is because stiffened panels have a larger load-bearing structural area and improved load redistribution capacity, reducing the localized stress concentration near the crack region. Additionally, the overall stiffness, characterized by the slope of the stress-strain curve, was only marginally affected by cracks. This is attributed to the stiffeners, which act as load-carrying elements, enhancing the global rigidity of the panel and delaying local instability by redistributing stresses away from the cracked region. Figure 12 presents the ultimate strength results for both longitudinal and transverse directions under varying crack sizes. In the case of transverse cracks, the ultimate strength decreased linearly with increasing crack size, showing minimal differences in strength reduction between transverse and combined cracks. However, when the crack size reached 50% of the panel's length (L) and breadth (b), the strength dropped suddenly. On the other hand, the longitudinal strength was more significantly influenced by the crack direction, with combined cracks showing a sharper decline. For crack sizes up to 25%, the longitudinal strength exhibited a near-linear reduction, with combined cracks starting at a value between the longitudinal and transverse results but showing a rapid decrease from 25%. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Crack Size** & **Intact** & **10\%** & **25\%** & **50\%** \\ \hline \multirow{3}{*}{Longi. strength} & \multirow{3}{*}{Trans. crack} & Present & 0.773 & 0.77 & 0.761 & 0.738 \\ \cline{3-6}  & & Equation (5) & 0.773 & 0.761 & 0.743 & 0.713 \\ \cline{3-6}  & & Difference & 0.000 & 0.012 & 0.024 & 0.034 \\ \hline \multirow{3}{*}{Trans. strength} & \multirow{3}{*}{Longi. crack} & Present & 0.293 & 0.291 & 0.29 & 0.286 \\ \cline{3-6}  & & Equation (5) & 0.293 & 0.263 & 0.22 & 0.146 \\ \cline{3-6}  & & Difference & 0.000 & 0.096 & 0.241 & 0.490 \\ \hline \end{tabular} Difference: (1 – Present/equation).  
\end{table} 
Table 4: Comparison of ultimate strength (\(\sigma_{u}/\sigma_{Y}\)) of cracked stiffened panels under uniaxial compressions with the existing formula. Figure 9: Effect of crack on ultimate strength of stiffened panel under uniaxial compression. Figure 10: Structural behavior of stiffened panel under longitudinal uniaxial compression. Figure 11: Structural behavior of stiffened panel under transverse uniaxial compression.