An A36 steel post is subjected to two forces P1 and P2 as sh

An A-36 steel post is subjected to two forces P_1 and P_2 as shown in the picture Two strain gauges are placed at point A (at 45 degree to each other as shown), the two gauges read epsilon_a =3.35 times 10^4 mm/mm and epsilon_b = 1.90 times 10^-4 mm/mm Determine the magnitudes of P_1 and P_2. P_1 =_____P_2 =_____A beam is made of southern pine having an allowable bending stress of sigma_allowable = 775 psi.

Solution

1) P1

Strain e = 3.35 * 10^-4

E = 200 Gpa

E = Stress / Strain

200 = Stress / 3.35 * 10^-4

Stress = 0.067 N/mm²

Stress = Load / Area

0.067 = P₁ / 2000

P_{1 =} 134 N

P_{2 =} 94 N