•Novel horizontal tying force method for robustness design of building structures.•Method anchored within rational framework considering sudden member/support loss.•Consideration of ductility limit, dynamic amplification and surrounding structure.•Treatment of beam/floor tying, different sources of tying and load combinations.•Verified effectiveness and simplicity as a replacement for prescriptive tying rules. This paper presents a rational method for the horizontal tying of multi-storey building structures aimed at robustness design and the mitigation of progressive collapse. Unlike current prescriptive tying force approaches, the new method benefits from i) a rational association with local damage scenarios consisting of the sudden loss of a column or a load-bearing wall, ii) the explicit consideration of the system ductility limit and dynamic amplification, iii) the systematic combination of various types of loading and sources of tying, and iv) supplementary methods for assessing the interaction of the affected floor system with the surrounding structure. Importantly, these relative benefits are still realised within a practical application framework that is comparable in simplicity to prescriptive tying rules, making the proposed tying method suitable for codification and as a replacement for prescriptive tying force requirements in the next generation of robustness design codes. Following a detailed exposition of the method formulation and parameters, the paper presents several studies which demonstrate the effectiveness of the proposed tying force method, concluding with an example that illustrates its application to a typical reinforced concrete floor system.