I have a basic question concerning strength and weight of materials. Please forgive me if my question is extraordinarily naive, but I'm an elderly retiree and my education is woefully lacking in this area. Thank you for your patience and understanding. Let us say we have a block of X material with dimensions 1 x 1 x 1. So it has a cross section of 1 and a volume of 1. Now, from the same base material, we produce a block with dimensions 2 x 2 x 2. It has a cross section of 4 and a volume of 8. Would it be correct to say block #2 has a tensile strength 4x greater than block #1, and a weight 8x greater than block #1? Is there some general rule that states that as an object is scaled up, its weight rises more steeply than its strength?
No, strength doesn't change. It is a material property independent on geometry. Strength is measured as force per unit area. What changes when you increase the cross section is the force necessary to break the material, not its strength. Strength to force is like density to weight. When we say that certain material is heavy or light weight we mean its density, i.e. weight per unit volume, not just its weight.
Let's say you have a piece of Aluminum 6061-T6, with cross section 1" x 1" (length does not matter). This alloy has a tensile (yield) strength of about 40,000 psi. This means you'd need to tie one end vertically to a rigid beam, and hang 40,000 pounds on the other end to barely deform this metal (yield strength is generally a +0.2% stretch point). If your cross section is 2" x 2", you would need 160,000 lbs. to do the same thing. The ultimate strength is always at or above the yield strength, and for this alloy is approx. 45,000 psi. This means you would need 45,000 pounds to actually break the 1"x1" bar. Note also that between applying the yield strength and the ultimate strength, the metal will neck down, reducing the effective area under stress, leading to a more rapid break. http://www.matweb.com/search/DataSheet.aspx?MatGUID=1b8c06d0ca7c456694c7777d9e10be5b&ckck=1 Compression strengths are generally close to tensile strengths in metals (but very different in say, concrete, where compression strength is high, but tensile is very low (thats why we add rebar)), but the actual usable compression strengths are also based on the geometry (length, solid .vs. pipe or tube, etc.), as the piece can buckle at a lower force than if you used a very short piece of material.