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  • Writer's pictureSi Shen

Stiffness, strength and ductility

Stiffness, strength and ductility are three crucial concepts in the understanding of structural behaviour, particularly in terms of seismic design. This blog post explains these concepts, by way of a linear-elastic-perfectly plastic structural behaviour model, for its simplicity.

Stiffness is the ability of the structure/material to limit deformation subject to an action. On a stress-strain diagram, it is represented as a slope. Stiffness is most pertinent to the serviceability of a structure, such as deflection, cracking and vibration. Usually, a stiffer structure is more desirable in serviceability, as it provides better comfort. In the context of seismic design, for frequent and low magnitude earthquakes, a high stiffness prevents the structure from high levels of deflection or discomfort, and reduces the damage to the non-structural part of the structure, e.g. partitions, equipment, façade.

Strength is to what magnitude of action the structure/material is able to resist without suffering permanent deformation (yielding). On a stress-strain diagram, it is represented by the level of the horizontal yield line. The higher the line is, the more strength there is. Another way to understand strength is that it is the tipping point where the behaviour of the structure steps out of the elastic zone and into the plastic zone (the turn from an inclined line into a horizontal line on the stress-strain diagram). Continuing with the seismic design example, when an infrequent and high magnitude earthquake hits, the structure is usually expected to sustain minor repairable damage (called the ‘damage control limit state’). From an analytical perspective, plastic hinges in the structure may form, i.e. part of the structure exceeds its design strength, but the structure should not collapse. The more plastic hinges form under the earthquake, the more damage is done to the structure; a structure with higher strength leads to less plastic hinges necessary to resist the earthquake. A key premise of plastic hinges forming in the structure is that there must be sufficient ductility - This brings out the next crucial concept.

Ductility is most pertinent to the design in disastrous events, such as catastrophic collisions (say hit by a heavy truck/ship/plane), extremely rare earthquakes, where large or unrepairable damage to the structure is acceptable, but the structure is expected to stand up to the disaster without collapsing. This allows timely evacuation of people inside the structure, saving their lives. From an analytical point of view, ductility allows a structure to deform permanently under an extreme action, and during this course absorbs/dissipates the energy from it (called ‘damping’). Crash-protection of modern cars is a classic example – when the car crashes into a brick wall, the front of the car is designed to have low stiffness and high ductility, so that it buckles and squashes upon impact, to absorb the impact energy, thus protecting the driver and passengers. On a stress-strain diagram, ductility is represented as the length of the yield (horizontal) line – the further it goes, the higher ductility the structure has. High ductility is almost always desirable, but it comes at a cost, so normally high ductility is only provided to the most crucial parts of the structure in terms of its overall stability.

A structure with low stiffness and high ductility can be safe enough but uncomfortable to use, whereas a structure with high stiffness but low ductility can be dangerous as it shows little signs of distress before it collapses, nor gives enough time for people to react in those situations. A bit more strength can never hurt, though we are obviously limited by material technology and construction costs.

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