Question

Aluminum (E = 70 Gpa) workpiece CE is clamped in place as shown here. This piece is 2-cm-tall and has a 0.5 cm x 1 cm rectangular cross-section. A 4-cm-long- steel (E = 200 Gpa), 1-cm-diameter bolt is adjusted to generate the workpiece clamping force. Assuming that member ABC is rigid, x = 4 cm, and the bolt is initially adjusted for no load in any member, what is the maximum stress in the bolt if the stress in the workpiece is not to exceed 200 MPa?

101 MPa 142 MPa O 162 MPa O 183 MPa

Answer 1

E_ alpha = 70 gpa E_ st = 200 gpa the force acting on the number CE F_CE = sigma_ CE A_ CE = 200 N/mm^2 times 0.5 times 1 alpha times 1 times 10 mm^2 = 10000 N F_CE = 10 KN delta_ CE = sigma_ CE L_CE/E = 200 times 2 times 10/70 times 10^8 N/mm^2 = 5.714 times 10^- 5 m since member ABC is rigid, delta_ BD = delta_ CE/2 Rightarrow 5.714 times 10^- 5/2 Rightarrow 2.86 times 10^- 5 m from simian finagler sigma_ BD = E delta_ BD/L_BD Rightarrow 200 times 10^9 times 2.86 times 10^- 5/4 times 10^- 2 = 142 N/mm^2 maximum stress in bolt sigma_ BD = 142 mpa