Answer to Question #144802 in General Chemistry for Joshua

Question

Two beams, A and B, made with the same material are to be subjected to a three-point bending test. Beam A has a dimension of 1.25 in x 2.5 in x 0.5 in while Beam B has a dimension of 1.5 in x 1.5 in x 0.75 in. Compare the respective fracture loads that will cause the beams to fail.

Answer 1

$\sigma$ f= 3p²/2bd²

^{Hence P=2bd2} $\sigma$f/3L

PA=2$×2.5×(0.5)2× \sigma$f/ $3×1.5$

$PA=0.33$$\sigma$f

$PB=2×1.5×(0.75)2×\sigma$f/$3×1.5$

$=0.38\sigma$ f

$=0.38\sigma$ f$>PA(0.33)\sigma$f