Hanging objects, referring to materials or components lifted and transported by tower cranes, require continuous monitoring, as undetected suspended loads can cause severe accidents and disrupt construction workflows. However, conventional vision-based detection models struggle to recognize the hanging state due to visual ambiguity and reliance on appearance without spatial reasoning. To address this challenge, this paper proposes a framework that leverages monocular depth information to infer the hanging state more effectively. The approach incorporates a depth-aware feature module, which captures depth differences and spatial context, and a segmentation-guided depth preprocessing that refines object boundaries. Integrated into baseline detectors, the proposed method significantly improves detection accuracy and reduces false positives in complex scenes. Experimental results demonstrate the value of depth-aware modeling and establish a foundation for reliable, state-aware detection of hanging objects, enabling automated monitoring and supporting more efficient management of lifting operations and site workflows in construction environments.