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A continuous and aligned fiber-reinforced composite is manufactured using 80 vol% aramid fiber (a kevlar-like compound) embedded nylon 6-6. A part for a high-performance aircraft utilizes this composite. If the part experiences 953 lb-f (pounds force) along the fiber alignment axis, what is the force conveyed by the fibers ?

Sagot :

nuhulawal20

Answer:

the force conveyed by the fibers is 947.93 lb-f

Explanation:

Given the data in the question;

V_f = 80% = 0.8

V_m = 1 - V_f = 1 - 0.8 = 0.2

Now,

length of fibre L_f = length of Nylon L_n

V_f = A_f × L_f = 0.8

V_m = A_n × L_n = 0.2

so

V_f/V_m = A_f/A_n = 0.8/0.2

A_f/A_n = 4

now, the strains in fibre is equal to strains in nylon

(P/AE)f = (P/AE)n

P_f/A_fE_f = P_n/A_nE_n

P_f = (A_f/A_n)(E_f/E_n)(P_n)    

P_f = ( 4 )( 131 / 2.8 )(Pn)  

P_f = 187.14Pn

and P_n = Pf / 187.14

Hence

given that P_total = 953 lb-f

P_f + P_n = 953

P_f + ( P_f / 187.14 ) = 953

P_f( 1 + ( 1 / 187.14 ) ) = 953

P_f( 1.00534359 = 953

P_f = 953 / 1.00534359

P_f = 947.93 lb-f

Therefore, the force conveyed by the fibers is 947.93 lb-f

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