Problem: To test various concrete mixtures, samples are made, allowed to cure for various times, and tested to destruction. A certain sample column is 72 cm long and 29 cm in diameter. High quality concrete has a compressive elastic (Young's) modulus of 30 GPa. (Concrete can't withstand much tension, so 30 GPa certainly does not apply to concrete in tension!) What is the change in length if the column is loaded with 45000 kg?
Solution: Substituting into the elastic modulus equation...
Comment: This appears to be a lot of distortion. In fact, high strength concrete can withstand about 40 MPa (this is what's commonly termed "6000 pound" concrete because 40 MPa is approximately 6000 pounds per square inch). The numerator - the stress - in this case is 6.68 MPa. So we're not too close to the ultimate strength of this concrete yet!
Further comment: All materials stretch or compress under load. Sometimes the amount is very evident, and yet it is safe. If you get the chance, stand on the walkway along the interstate where it crosses the Delaware River. As the big trucks go by, you can feel and see the bridge move up and down!