Understanding Yield Lines Theory Applied to Ground Supported Slabs

Industrial floors are subjected to different types of loads — point, line, and uniformly distributed. These loads cause the slab-on-ground to act in flexure or shear. TR34 provides guidance and verification procedures to ensure that neither of these modes of behavior exceeds the slab’s capacity.

In the case of flexure induced by point loads, checks of industrial slabs on ground to TR34 relies on the yield-line theory.

Unlike simplified or purely elastic hand-calculation, yield-line theory is a plastic limit-analysis method that assumes the slab forms fully developed yield lines (or mechanisms) at collapse, allowing the estimation of its ultimate load-carrying capacity.

The flexural capacity of the slab against point loads depends on its maximum admissible sagging and hogging moments, \( M_p \) and \( M_n \).

\( M_p \) is the positive (sagging) moment that tends to crack the lower face of the slab, pushing it against the subgrade. Its calculation assumes a fully plastic behaviour and represents a true Ultimate Limit State (ULS) verification, accounting for the contribution of reinforcement and/or fibres.

\( M_n \) is the negative (hogging) moment that tends to crack the upper face of the slab, lifting it from the subgrade. TR34 limits Mₙ to the resistance of unreinforced concrete in order to prevent visible surface cracking; therefore, it corresponds to a Serviceability-type verification.

Once \( M_p \) and \( M_n \) are determined, they are applied within the yield-line mechanism equations to estimate the maximum admissible point loads with respect to bending of the slab.

Our calculation reports always show you the hogging and sagging moments of your slab, and base further calculations on them.

The resistance of your slab to loads is different depending on where they are applied. TR34 differentiate between loads that are applied in the center, edge and corner of panels delimited by joints.

The slab’s capacity is highest when loads are applied to the center of panels. It is lowest when loads are applied in the corners of the panels.

Slabs’ capacity to withstand loads that are applied internally on panels can be improved by putting more reinforcement (mesh / fibers), increasing slab thickness, upgrading concrete class or improving the subgrade stiffness.

However, when loads are applied on edges and corners of slab panels, putting in more reinforcement will not help. Here you can only increase your slab thickness, upgrade your concrete class or improve your subgrade stiffness. Additionally, you can consider the use of dowels, which are devices that allow the transfer of a part of the load across joints and make two panels work on it instead of only one.

Our app lets you design and include dowels in your slabs.