Final Review

I posted a copy of my old final to my blog, so you will have an example of to expect. The final is 6 problems (worth 20 pts apiece). So no one problem will be worth more than the other.

You can expect two the problems to be

• Shear and Bending Moment diagrams - Solving the problem using either equations or the intergration method (sum of areas). You will need to draw the free-body diagram, solve the reactions, and compute the shear diagram and bending moment diagram. You will need to know how to find the slope of the curves and the maximum and minimum shear force and bending moment. You will find additional examples at last semester's CE 202 page. You will find them in assignments 28, 29, 30 and 31. The assignments from this semester are assignments 38, 39, and 40.
• Hydrostatic problem - Solve for reactions on gate, compute the location of the forces, the total force due to weight of the water, etc. Know why you do not need to use the atmospheric pressure in computing reactions. You will find additional examples at last semester's CE 202 page. Assignments 40, 41, and 42. The assignment from this semester is 41.

Possible topics for

• Vectors - Finding the vector along components, cross products, dot products. Using the information to find the force vector along a line. Determinining the angle between two vectors, direction cosines and mixed triple products (U*(V x W)). You will find additional examples at last semester's page. Assignments 1 ,2 ,3 and 4. The results from this semesters problems are assignments 1, 2, 3, and 4.
• Sum of Force - Solving problems from spring forces, contact forces and systems of forces. We dealt with 2-D and 3-D equilibrium problem (sum of forces = zero). W= mg and development of coordinate systems and free-body diagrams. The assignments were 5, 6, and 7. The material from last semester are assignments 5 and 6.
• Sum of Moments - Solving equilibrium equations (sum of forces and sum of moments) in 2-D and 3-D. Computing the moment about a line, couples, wrenches, magnitudes of moments and resultant moments. The assignments were 8, 9, 11, 12, 13, 14, 15, and 16. The assignments from last semester's homework are 7, 8, 9, 11, and 12.
• Computing equilibrium equations in 2-D and 3-D. You will have at least 1 problem dealing with equilibriums. We covered this material in assignments 17, 18, 19, 20, and 21. The previous semester was covered in assignments 14, 15 and 16.
• Truss members - Truss have no moments in the members, the members are either in tension or compression. We solved the problems using the method of joints and using the method of sections. We covered the material in assignments 23, 24, and 25. The previous semester was covered in assignments 17, 18, 19, and 20.
• Frames and Machines and Mechanisms - These items do have internal moments and we need to solve the problems by breaking them into parts and solving the components. Look at things such as pulleys and realize that the tension is constant unless friction is involved. Know how to recognize two force members(members which are either in tension or compression). You recognize it by not having a force acting perpendicular to the main axis. We covered this material in assignments 26, 27, and 28. The previous semester, it was covered in assignments 21,22, and 23.
• Centroid and Distributed Load - Compute the center of an object and computing distributed loads and finding equivalent force and location. We covered this in assignments 29 and 30. The previous semester it was covered in assignments 13 and 37.
• Moments of Inertia - Compute the moments of inertia for an object using integration and computing moments of inertia using the parallel axis theorem for composite members. We covered the material in assignments 31 and 32. The previous semester was covered in assignments 38 and 39.
• Friction forces - Compute the resistance due to friction. Friction opposes the motion of the object. One needs to compute the normal force to find the maximum friction force. The assignments related to this topic were 33 and 35. The previous semester's assignments were 32, 33, and 34.
• Friction of belts and ropes over a bar. Computed the resistance due to a rope or belt sliding over a bar. We covered this in assignment 36. The previous semester, it was covered in assignment 36.
• Internal Forces - Compute the internal forces in a mechanism or frame. One needs to know how to compute the reactions, free-body diagrams, and recognize two force members. Find P, V, and M. Know positive and negative shear and bending moment. We covered this material in assignment 37. The previous semester assignments 26 and 27 covered the material.

Remember that one of the most important concepts of this course is free-body diagrams. So if you can draw a free-body diagram to solve the problem, you better have one.

There are copies of old exams from previous semester with solutions, exams 1, 2, 3, and 4. Our exams are 1, 2, and 3. I will post exam 4 solution on Friday.

Have fun.

Homework - Solutions

I have posted the last of the homework solutions sets. So can get them off of the lecture page. You can find the complete set of homework solutions. My grader has finished grading the last of the homework and I will have them tomorrow in class.

Final Exam -example

This is the final that I gave last semester.

Final - Fall 2004


I will post a review for the final later today along with the solution to homeworks 40 and 41.

Exam 4 - Question

I took you practice test #4 and could not figure out how you solved for the reaction at R_d. I used your exact numbers and the answer came out less than what you had written down.

The 1/2 * (11 kN/m³) (3 m)*(2 m)*(1 m) should be (11 kN/m³) (3 m)*(2 m)*(1 m) because you are dealing with the rectangular section, when I cutted and pasted I left in the 1/2.

Also on the friction problem on the same test why do you have to solve for the tipping force in order to get the right tension for T₂ and T₃.

The force required to slide the block was 60 N, however in order to tip the block it is 56.25 N, therefore the block will tip before it slides.

Exam 4 - Review

The exam will consists of three questions with same format as the last three exams. The first two questions will be worth 35 pt and third 30 pt. It is open book and open notes. We covered three main topics since the last exam.

1. Find the characteristics of shapes: the centroid, x bar and y bar, moment of inertia, I_x and I_y, and the radius of gyration, k_x and k_y. The moment inertia can be around center of the object or it can be about a given axis, this is handled by the d_i = y_i - y₀ or d_i = x_i - x₀. The x_i and y_i are the center of the component and x₀ or y₀ is the location of the desired axis. You will need to know how to find the components for a composite body. The problems related to the topic: Assignment 29, Assignment 30 ,Assignment 31, and Assignment 32
2. Another problem will cover friction acting on surfaces between two objects and friction over a bar. Remember that friction will opposite the motion. Draw the free-body diagrams! The problems related to the topic: Assignment 33, Assignment 35, and Assignment 36 .
3. The last topic is internal forces, determine the shear force, V_A, the axial force, P_A, and the bending moment, M_A. You will need to know how to solve for the reaction of a system whether a beam or a mechanism. Draw your free-body diagrams. The problems related to the topic: Assignment 37 and Assignment 38.

You can find additional examples of homework at CE 202 - Fall of 2004 look at problem sets for internal forces ( Assignment 26 and Assignment 27 ), frictional forces (Assignment 32, Assignment 33, Assignment 34 and Assignment 36) and characteristics of bodies (Assignment 37, Assignment 38 and Assignment 39 ).

Old Exams

I have two old exams from previous semester.

CE 202 - Fall 2004

Exam3 solution

Exam4 solution

Statics and Dynamics Course (TAMU) -static portion of the class

EXAM1 solution

EXAM2 Fall

Problem 10.43 & 10.45 - Solution

I have posted a series of shear and bending moment diagrams at Assignment39-solution .

Problem 10-28

I am having trouble with problem 10.28. I don't understand how the book is getting 50lb - 25/3(x-6)^2 for the shear force. I understand were the 50 lb force is coming from I just don't understand how to make the equation.

When you are dealing with a ramp function

w(x) = (100 lb/ft /6 ft) x

V(x) = 50 lb	-	1/2	(100 lb/ft /6 ft) (x-6ft) *	(x-6 ft)
		triangle	height	base

Example Problems

If you are having problems with the ramp load you might want to take a look at the set of example problems I posted to the lecture page.

You can connect to them by

http://www.unm.edu/~esandt/Teach/Homework/Example38.doc

Problem 10.31 - Solution

Equations for problem 10.31

0 m £ x < 0.2 m

V(x) = 250 N
M(x) = 250 N(x)

0.2 m £ x < 0.3 m

V(x) = 1750 N - 7500 N/m (x)
M(x) = 1750 N(x) - 3750 N/m (x²) - 150 N-m

0.3 m £ x < 0.375 m

V(x) = -500 N
M(x) = -500 N(x) + 187.5 N-m