contestada

A fabric used in air-inflated structures is subjected to a biaxial loading that results in normal stresses sx 5 18 ksi and sz 5 24 ksi. Knowing that the properties of the fabric can be approximated as E 5 12.6 3 106 psi and n 5 0.34, determine the change in length of (a) side AB, (b) side BC, (c) diagonal AC

Respuesta :

Answer:

δab = 0.003124 in

δbc = 0.0042572 in

δac =  0.00505 in

Step-by-step explanation:

Given:

- σ z = 24 ksi   , σ x = 18 ksi

- E = 12.6 * 10^6 psi

- v = 0.34

Find:

a) δab

b) δbc

c) δac

Solution:

- Compute strains:

                    εx = (σx - v*σz) / E = (18,000 - 0.34*24,000)/(12.6*10^6)

                    εx = 780.95 * 10^-6

                    εz = (σz - v*σx) / E = (24,000 - 0.34*18,000)/(12.6*10^6)

                    εz = 1.41905 * 10^-3

- Compute δab and δbc:

                    δab = εx*AB = 780.95 * 10^-6 * 4 = 0.0031238 in

                    δbc = εz*BC = 1.41905 * 10^-3 * 3 = 0.0042572 in

- Compute δac by using component of δab and δbc:

                   δac = sin(Q)*δab + cos(Q)*δbc

                   δac = (4/5)*0.0031238 + (3/5)*0.0042572

                   δac = 0.00505 in

Otras preguntas