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Fundamentals

Stiffness and Strength

Stiffness refers to the amount of deformations under the applied load. Strength, on the other hand, represents how much load the member can resist before it fails.

Consider a piece of chalk and a piece of rubber with the same cross-section and length. If we try to bend the piece of chalk it does not deform much but it breaks due to its low tensile strength. Therefore, chalk has large stiffness but low strength. On the other hand, the piece of rubber easily bends but doesn’t break or fail even if it is folded. Therefore, compared to chalk rubber has low stiffness but high strength. In addition, since the failure of chalk happens suddenly without much deformation (strain), it is called a “brittle material”. On the other hand, rubber is a "ductile material". As an analogy, steel behaves more like rubber, and concrete or masonry more like chalk.

 

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Deformation of a Brittle Material

 

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Deformation a Ductile Material

Stiffness generally depends on the modulus of elasticity, and strength depends on the material’s  yield strength or its equivalent. For a beam (bending member) stiffness also depends on its moment of Inertia (I) and length. To increase stiffness (to reduce deformation under load) it is most effective to make the member deeper (larger h) since increasing depth rapidly increases the moment of inertia (l=bh3/12 for a rectangular shape). For a rectangular beam, b is the width, and h represents the depth.

 

 

 

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