Bonus Points Opportunity.
Bonus Points Opportunity
These points will be added to your raw Test 1 score out of 50
The purpose of this assignment is two-fold. First, it is to give you a chance to earn an extra 15 points
that will be added to your raw Test 1 score out of 50. Second, since we will soon be learning finite elements
of beams and frames, we need to refresh our knowledge of shear force and bending moment diagrams that
we learnt in prior classes. Please follow the instructions below:
1. This is a strict “No Collaboration Whatsoever” assignment. i.e., Type-I. You will need to include an
honor pledge that you did this work entirely on your own, without assistance from other humans, and
without assistance from solutions from prior semesters.
2. Note that solution hints are included at the end of this assignment.
3. Create a new folder on your computer. Give this folder a name which includes your last name. Place in
this folder your MATLAB files, along with a README.txt file that tells us how to run your program.
4. Include in the README file your honor pledge that you did this work on your own. Assignment will
NOT be graded if the honor pledge is missing.
5. Create a “zip” archive of this folder, and upload on Blackboard.
Design of the optimum support location for a beam
The beam AB shown above is hinged at B and is supported by a roller at D. This support D is to be
designed to carry a load uniformly distributed from its end A to its midpoint C with maximum efficiency.
The objective here is to find the best location for the support D, i.e., to find the best value of the distance
a (which we will call a
The design will be optimum when you place the roller support D such that the maximum of the absolute
value of the bending moment in the beam is minimized.
i.e., your design should be such that the peak of the bending moment magnitude is as small as possible.
Note that the bending moment M(x) varies with x along the length of the beam from A to B.
Your task list
Write a MATLAB program to solve this problem. Your MATLAB program should report all of the following:
1. the optimum location of the support, i.e., a
2. the corresponding absolute value of the maximum bending moment,
3. the location along the beam where this extreme value of the bending moment is attained,
4. a plot of the bending moment diagram for this optimum support location.
Solution hints are on the next page.