SLM wrote:havenguy wrote:I have another question about stiffness. We used the stiffest peices of wood for our tower for states, and our tower ended up weighing about 2 grams more than our previous ones. So does more stiffness mean greater mass?
In structural engineering, stiffness is defined as the quantity that relates displacement to force in a member.
For example, if a member is subjected to an axial force (either compression or tension), then the relationship between the axial displacement (shortening or elongation of the member) and the force can be written as:
F = k d
where F is the axial force, d is the axial displacement and k is the stiffness coefficient of the member.
From the above equation, you can see that the stiffer the member (the larger the coefficient) the less the member is going to displace when it is subjected to the force F. This concept also applied to buckling; the stiffer the member, the larger the force has to be to cause the member to buckle (to displace).
But how is stiffness related to the weight of a member?
In general, an stiffness coefficient is determined based on several properties of the member such as its size and its modulus of elasticity. For wood, since modulus of elasticity is directly related to wood density, then we know that stiffer members have a higher density. And since, a member's weight is directly related to its density, then the denser the member, the more it weighs.
Alright, a bit confusing, but denser members means greater stiffness, resulting in greater mass. That makes sense. Thanks