Since 1996, web accessibility evaluation has been an important aspect of web development to increase social inclusion for people with special needs. Several web accessibility evaluation and testing tools have been developed to automatically evaluate websites in order to identify barriers for people with disabilities. The developed tools are significant since their aim is to effectively represent accessibility issues. However, a few issues with website accessibility cannot be identified through the existing accessibility testing tools due to several limitations, including (i) inappropriate guideline selection, (ii) ambiguities in guideline understanding, (iii) avoiding user and expert suggestions as evaluation criteria, (iv) limited consideration of semantic perspectives, and (iv) unwillingness to incorporate the updated engineering methods. Therefore, reported results may be unclear and inappropriate for some users. Such limitations are critical factors that reduce the effectiveness of the developed tools. These issues cause unwillingness to use a particular tool or possible adoption of other tools. In this situation, we must identify which aspects are important to incorporate in the development in order to make the developed solution more effective as it allows users to make their website accessible to people with disabilities. In this paper, first, we present a literature review of different existing solutions for web accessibility testing to identify their challenges and limitations. Following the reported findings, we propose an automated web accessibility evaluation framework addressing several accessibility aspects to improve the evaluation results by mitigating the limitations of existing solutions. The proposed framework is validated by comparing it with existing automated solutions considering their functional properties. The proposed accessibility framework might be beneficial for web developers, accessibility engineers, and other practitioners to incorporate into their development and research.