Construction remains one of the most hazardous sectors. Recent advancements in AI, particularly Large Language Models (LLMs), offer promising opportunities for enhancing workplace safety. However, responsible integration of LLMs requires systematic evaluation, as deploying them without understanding their capabilities and limitations risks generating inaccurate information, fostering misplaced confidence, and compromising worker safety. This study evaluates the performance of two widely used LLMs, GPT-3.5 and GPT-4o, across three standardized exams administered by the Board of Certified Safety Professionals (BCSP). Using 385 questions spanning seven safety knowledge areas, the study analyzes the models' accuracy, consistency, and reliability. Results show that both models consistently exceed the BCSP benchmark, with GPT-4o achieving an accuracy rate of 84.6% and GPT-3.5 reaching 73.8%. Both models demonstrate strengths in safety management systems and hazard identification and control, but exhibit weaknesses in science, mathematics, emergency response, and fire prevention. An error analysis identifies four primary limitations affecting LLM performance: lack of knowledge, reasoning flaws, memory issues, and calculation errors. Our study also highlights the impact of prompt engineering strategies, with variations in accuracy reaching 13.5% for GPT-3.5 and 7.9% for GPT-4o. However, no single prompt configuration proves universally effective. This research advances knowledge in three ways: by identifying areas where LLMs can support safety practices and where human oversight remains essential, by offering practical insights into improving LLM implementation through prompt engineering, and by providing evidence-based direction for future research and development. These contributions support the responsible integration of AI in construction safety management toward achieving zero injuries.