statics take home test

Fall 2018 Statics Mid-Term Exam 3 Take-Home Name:

Please show all free body diagrams and the corresponding equilibrium equations that you use. Neat

freehand sketches are fine. Write the general forms of the equilibrium equations (ΣFX = 0, ΣFX = 0, ΣMA =

0) first before writing out the forces and moments specific to that problem. The paper is out of 100

points, and there are 25 bonus points including the extra credit question.

1) If a 200 N force is applied on the cutting tool as shown, determine the corresponding force

acting at point E. (Hint 1: Remember that each component of a machine is a rigid body and

every component must be in equilibrium, Hint 2: Write out all the equilibrium equations for

each component first, that will direct you at how to solve for the unknown forces, Hint 3: Use

equilibrium equations that you did not use for solving as a check). (20 points)

2) Solve for all the joint forces in the following frame. The suspended bob has a mass of 100 kg.

Note that member ABDF is one monolithic member. (20 points)

3) For the beam shown below, draw the bending moment and shear force diagrams. You could

use either the short procedure shown in class, or the full calculation, either is okay. Either way,

please label the values of the bending moments and shear forces at points where the graph

changes shape. (30 points)

4) For the cable given below, the total length is given to be 35 feet. Determine the reactions at the

supports A and B, and the tension values in each of its segments. (Hint: Since the total length of

the beam is given, use pythogorean triplets to figure out the coordinates of point C, at which the

load acts). (20 points)

5) Draw the free body diagram for one simple structure (machine, frame, truss etc.) that you use in

daily life directly or indirectly. Make sure to reduce it to the most basic form possible, showing

only required geometry and joints. (2D idealization would be fine, 3D is okay too). Show the

free body diagram for the entire structure as well as the free body diagrams for each of the

component members. Make sure to include applied loads. (Examples: pliers, idealized frame of

your apartment/house, door frame, wall-mount frame for TV/Pictures etc., dining table). (20

points)

Extra Credit: Using the reactions obtained in problem 2, draw the axial force diagram, shear force

diagram, and bending moment diagram for members ABDF and ECD. (15 points)

25 kips

9 m 16 m

A B