The model of housing based on the religion of Islam in order to create a residence and obtain peace for the family depends on responding to their fixed and changing needs. Considering that the housing body is a container in which the family community is formed, the need to adapt the housing to the growth of the family as changing needs and respond to it over time in order to achieve the stability of the family community is important. In the meantime, the "expansibility" can be effective in climate stability in addition to social stability by making adaptations or changes in housing components according to the changing needs of residents. Given the high consumption of fossil fuels, designing and constructing residential buildings compatible with the climate is essential in order to reduce energy consumption. In fact, the use of private courtyards on the floors of residential units, in addition to creating a platform for the development of building walls, helps to provide light to the interior spaces and control the climatic conditions. The aim of the present research is to identify the optimal model of social-climatic expandable housing that is suitable for the growth of the family. In this way, the research question was formed in search of a housing model that, in addition to the expandability of the housing components in the courtyard of the apartment, also provides climate efficiency. This article focuses on the topic of social sustainability in housing by examining the expansion of its components in the courtyard of the apartment and it also addresses the topic of climate sustainability by assessing the amount of radiation received by expansible walls in the courtyard. The use of both qualitative and quantitative methods to identify the social-climatic expandable housing pattern has led, in the first stage, to the presentation of the expandable patterns A, B, and C in the courtyard of a residential apartment. Then, based on quantitative methods with simulations of the patterns in EnergyPlus software, the optimal pattern was identified. As the main result of this research, by comparing the amount of radiation received from the south, east and west in the cold, moderate and hot months of the same direction units, the best units in the SW direction belong to building B, in the NE and NW direction belong to building C, in the SE direction It belongs to A and C buildings.
