Explanation Given information: The three uniform links of the mechanism has a length L and weight W . The spring always remains vertical, and is un-stretched when θ = sin − 1 ( 8 W k L ) _ . Assumption: Consider the state of member as tension where the force is pulling the member and as compression where the force is pushing the member. Consider the force indicating the right side as positive and left side as negative in horizontal components of forces. Consider the force indicating upward is taken as positive and downward as negative in vertical components of forces. Consider clockwise moment as negative and anti-clock wise moment as positive wherever applicable. Apply the Equation of equilibrium wherever applicable. Geometry: Show the free-body diagram of the geometry as in Figure 1. Using Figure 1, Determine the spring stretches using the geometrical equation. x = L 2 sin θ Determine the force in the spring using the relation. F s p = k x (I) Here, the stiffness is k and the stretch is x . Substitute L 2 sin θ for x in Equation (I). F s p = k × L 2 sin θ F s p = k L 2 sin θ Segment BC : Show the free-body diagram of the segment BC as in Figure 2. Using Figure 2, Moment about point B : Determine the horizontal reaction at point C by taking the moment about point B . ∑ M B = 0 C x ( L ) = 0 (II) Along the horizontal direction: Determine the horizontal reaction at point B by resolving the horizontal component of forces. ∑ F x = 0 C x − B x = 0 (III) Along the vertical direction: Determine the vertical reaction at point B by resolving the vertical component of forces. ∑ F y = 0 B y − C y − W = 0 (IV) Conclusion: Solve Equation (I). C x = 0 Substitute 0 for C x in Equation (III). 0 − B x = 0 B x = 0 Segment DC : Show the free-body diagram of the segment DC as in Figure 3. Using Figure 3, Moment about point D : Determine the vertical reaction at point C by taking the moment about point D . ∑ M D = 0 C y ( L cos θ ) − W ( L 2 cos θ ) = 0 (V) Conclusion: Solve Equation (V)

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Question

Chapter 6.6, Problem 111P

To determine

The angle θ for equilibrium.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.6, Problem 110P

Chapter 6.6, Problem 112P

Students have asked these similar questions

Qu. 13 What are the indices for the Direction 2 indicated by vector in the following sketch? Qu. 14 Determine the indices for the direction A and B shown in the following cubic unit cell. please show all work step by step from material engineering

The thin-walled open cross section shown is transmitting torque 7. The angle of twist ₁ per unit length of each leg can be determined separately using the equation 01 = 3Ti GLIC 3 where G is the shear modulus, ₁ is the angle of twist per unit length, T is torque, and L is the length of the median line. In this case, i = 1, 2, 3, and T; represents the torque in leg i. Assuming that the angle of twist per unit length for each leg is the same, show that T= Lic³ and Tmaz = G01 Cmax Consider a steel section with Tallow = 12.40 kpsi. C1 2 mm L1 20 mm C2 3 mm L2 30 mm C3 2 mm L3 25 mm Determine the torque transmitted by each leg and the torque transmitted by the entire section. The torque transmitted by the first leg is | N-m. The torque transmitted by the second leg is N-m. The torque transmitted by the third leg is N-m. The torque transmitted by the entire section is N-m.

Please help, make sure it's to box out and make it clear what answers go where...

Chapter 6 Solutions

Engineering Mechanics: Statics

Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 3FP Ch. 6.3 - Determine the greatest load P that can be applied...Ch. 6.3 - Identify the zero-force members in the truss....Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P Ch. 6.3 - Determine the force in each member of the truss,...Ch. 6.3 - Determine the force in each member of the truss,...

Knowledge Booster