Solid mechanics problem (pretty much a static problem)

In summary, the problem involves determining the reactions at the pin supports at A and E and the axial forces in members AB, AD, and DE in a pin-jointed truss ACE that is part of a cable-hoist system. The weight of the cargo box being lifted is 1500 b and the weight of the cables is neglected. To solve the problem, basic statics equilibrium equations and resolving forces into components are used. The main difficulty lies in incorporating the moment caused by the tension in the cable. By resolving the forces and summing moments about a point, the values for the reactions and axial forces can be determined.
  • #1
DyslexicHobo
251
0

Homework Statement


A pin-jointed truss ACE is part of a cable-hoist system that is used to lift cargo boxes, as shown in Fig P1.4-5. The cable from the lift motor to the cargo sling passes over a 6-in pulley that is supported by a frictionless pin at C. The weight of the cargo box being lifted is 1500 b. Neglecting the weight of the cables, determine the reactions at the pin supports at A and E, and determine the axial force in each of the following members: F1 (in member AB), F2(in member AD), and F3 (in member DE). Explain the answer you got for the value of F2.


Homework Equations


Pretty much all the basic statics equilibrium equations. (Sum of F_x=0, F_y=0, M_z=0)


The Attempt at a Solution


I drew up a picture, but the main problem I'm having is how to deal with the sum of the moments. It's been a while since I've done any statics problems, so I'm unsure of how to incorporate the moment that the tension in the cable causes. I think I can find out everything else the question asks once I get past this small hurdle.
 

Attachments

  • Homework14.5.jpg
    Homework14.5.jpg
    26.5 KB · Views: 538
Last edited:
Physics news on Phys.org
  • #2
DyslexicHobo: Preferably reverse the direction of reaction force Ft in your diagram, if you wish. You know the magnitude of Ft is equal to the cable tension, right? And you know the direction of Ft. Resolve Ft into components Ftx and Fty. You know reaction force Fe is collinear with member DE, right? Resolve Fe into components Fex and Fey. Now sum moments about any point you wish.
 
  • #3


I would approach this problem by first identifying and defining all the variables involved, such as the weight of the cargo box, the lengths and angles of the truss members, and the forces acting on each member. I would then use the basic statics equilibrium equations to set up a system of equations and solve for the unknown variables. In this case, the sum of the moments equation would involve the tension in the cable, which can be calculated using the weight of the cargo box and the angle of the cable over the pulley. From there, I would use the equations to solve for the reactions at A and E, as well as the axial forces in each member.

For F2, the axial force in member AD, I would expect it to be zero since it is a zero-force member. This means that it does not contribute to the stability or equilibrium of the truss and can be removed without affecting the overall structure. This is because the forces acting on this member are parallel and equal in magnitude, resulting in a net force of zero.

Overall, the solution to this problem would involve using a combination of equations, calculations, and logical reasoning to determine the reactions and forces in the truss. It is important to carefully consider all the forces acting on each member and how they contribute to the overall equilibrium of the system.
 

1. What is a solid mechanics problem?

A solid mechanics problem is a type of engineering problem that involves analyzing the behavior of solid materials when subjected to external forces. It is a branch of mechanics that focuses on the study of the deformation and stability of solid structures.

2. What are the main types of solid mechanics problems?

The main types of solid mechanics problems are static, dynamic, and fatigue problems. Static problems involve analyzing the behavior of structures under external forces at rest, while dynamic problems involve the study of structures in motion. Fatigue problems involve the analysis of the failure of materials under repeated loading and unloading cycles.

3. How do you approach a solid mechanics problem?

The first step in approaching a solid mechanics problem is to clearly define the problem and identify the relevant parameters, such as material properties, external forces, and boundary conditions. Next, one should choose an appropriate mathematical model and use equations and principles of mechanics to solve for the unknowns. Finally, the results should be verified and analyzed to ensure they are physically realistic.

4. What are some common challenges in solving solid mechanics problems?

Some common challenges in solving solid mechanics problems include dealing with nonlinear material behavior, complex geometries, and boundary conditions, as well as the need for accurate and reliable experimental data to validate the results. Another challenge is the computational complexity involved in solving large-scale problems.

5. How is solid mechanics used in real-world applications?

Solid mechanics is used in a wide range of real-world applications, including structural engineering, aerospace engineering, automotive engineering, and biomechanics. It is essential for designing and analyzing structures such as buildings, bridges, and aircraft, as well as for understanding the behavior of materials in medical devices and prosthetics. Additionally, solid mechanics is crucial for predicting and preventing failures in various structures and machines.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
974
  • Introductory Physics Homework Help
Replies
2
Views
935
  • Introductory Physics Homework Help
Replies
5
Views
4K
Replies
5
Views
808
  • Introductory Physics Homework Help
Replies
8
Views
7K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
12K
  • Introductory Physics Homework Help
Replies
5
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Mechanical Engineering
Replies
2
Views
901
Back
Top