Dr. Z’s Corner

Dr. Z

Ahmet Zeytinci, P.E., Ph.D., Fellow-NSPE, Fellow-ASCE is an award-winning professor, structural engineer, author and mentor living in Washington, D.C. Since joining academia, "Dr. Z", as he is known by his students and colleagues, has distinguished himself on campus and beyond. He is passionate about engineering, gifted in teaching, and is a true champion for professional licensure. Dr. Z. has extraordinarily high standards; has produced award-winning designs; is prolific in professional service; and infects others with these same values. He is the recipient of numerous local, regional and national awards, including recent national awards from the National Society of Professional Engineers (NSPE) and American Society for Engineering Education (ASEE). Since 2014, he has been regularly writing monthly articles for “Dr.Z’s Corner “ and offering hundreds of engineering problems, for free, every month for students, engineers and engineering educators worldwide. Dr. Z. also offers pro-bono Saturday classes for students and engineers; his free classes are open to all in the greater Washington metro area and cost nothing, nada, zilch! Starbucks coffee is always a must have for Dr. Z.

Dr. Z's Corner

Dr. Z’s Corner (201602)

A Picture is Worth a Thousand Words:
Demystifying the Shear Force and Bending Moment Diagrams

By Ahmet Zeytinci, P.E., F-NSPE



It is no secret that I received all my degrees from Istanbul Technical University (ITU), founded in 1773. ITU is one of the premier engineering schools in Europe, and back in the early 1970s, we had about 150 full-time faculty members and support staff in our Civil Engineering department. For my doctoral research, I was working on a highly mathematical problem on vibrations of plates and one of my Ph.D. advisors was a professor who worked with the well-known scientist Richard Edler von Mises at Harvard University while completing his PhD. Some of my readers may also remember von Mises who defined the yield criterion that suggests that the yielding of materials begins when the second deviatoric stress invariant J2 reaches a critical value. As I reflect on my 40-year career in structural engineering, it is remarkable to see how the landscape has changed, while some knowledge and educational tools that I learned from my mentors are priceless and I use them in my classes every day. Today we will focus on shear force (V) and bending moment (M) diagrams. Many students struggle when they try to draw their first shear and moment diagrams.

In structural engineering, we are interested in the analysis and design of beams or structural members supporting concentrated and/or distributed loads that are mostly perpendicular to the axis of the members. In practice, beams are usually long, straight, and prismatic and such transverse loadings would cause only bending and shear forces. When the loads are not perpendicular to the member, they also produce axial forces as well. The concentrated loads may be expressed in newtons (N), pounds (lb), or their multiples, kilonewtons (kN) or kips. Distributed loads are generally expressed in N/m, kN/m, lb/ft or kips/ft. A shear force diagram (V) is a graph in which the abscissa (horizontal reference axis) represents distances along the beam length, and the ordinates (vertical measurements) represent the transverse shear at the corresponding beam section. A moment diagram (M) is a graph in which the abscissa represents distances along the beam and the ordinates represent the bending moment at the corresponding sections. Shear and moment diagrams can be drawn by calculating values of shear and moment at various sections along the beam and plotting enough points to obtain a smooth curve. Such a procedure is rather impractical and time consuming.

Right at this point, I remember my Ph.D. advisor’s words, “A well-drawn (V) and (M) diagram is like ‘poetry’ for some of us and you have to feel them without doing any number crunching.” My colleague Vagelis did just that for our readers and prepared a dozen beautiful diagrams using his well-known software, Beam-2D as shown in the Problem Section this month.

For the sign conventions, positive moment generates a curvature that tends to hold water (concave-upward curvature) or moment creating tension in bottom fibers of beam, whereas negative moment causes curvature that sheds water (concave-downward curvature). For the sign of shear, positive shear is the upward shear to left. This is a standardized and universally accepted convention. Because the convention is related to the probable deflected shape of the beam for a prescribed loading condition, it may be helpful to intuitively sketch the beam’s deflected shape to help in determining the appropriate signs. With the aid of such diagrams, the magnitudes and locations of various important quantities like Mmax become immediately apparent. The maximum moment Mmax occurs at places where shear = 0 or V changes sign. It is convenient to draw these diagrams directly below the free-body diagram of the beam using the same horizontal scale. Why these diagrams are so important? Because by using these diagrams, an engineer can see, at a glance, the performance requirements of a structural member at every section.

Finally, we have to remind our readers that FE and PE are very fast-paced exams and you will have little time to look up information. Therefore, make sure you are familiar with your reference material and begin with the subject areas you know best. This will give you more time and build your confidence.

Most importantly, stay relaxed and confident. Always keep a good attitude and remind yourself that you are going to do your best!

Until next time,

Ahmet Zeytinci, P.E.

This email address is being protected from spambots. You need JavaScript enabled to view it.

Dr. Z’s Corner (201601)

ASCE-2016 Centennial Celebration:
Dr. Z’s Corner & Exciting New Features

By Ahmet Zeytinci, P.E., F-NSPE



Our readers may know by now the “Outstanding Website Award” winner, the NCS is celebrating its 100th year in 2016. Accordingly, all activities, including our column, will have a centennial focus this year. You may have already noticed the new look and user-friendly functionality of the new Dr. Z’s Corner. This major overhaul was the result of a great teamwork of many individuals at the NCS, the Board members, Scott, Chris, Ranjit, Rachel, L.J., and my good friend Prof. Dr. Vagelis Plevris from Greece. I would like to thank each of you for your dedication to the profession and commitment to engineering students and practicing engineers not only in the Washington metro area but also in the nation and around the globe.

Now with the new features of Dr. Z’s Corner, our readers will have easy access to all timeless articles, past issues, hundreds of original problems, solutions, tips, and applications with a click of a mouse. Once www.asce-ncs.org is entered, the readers will see the NCS’s beautiful centennial logo on the top left of the menu bar and “Special Features” on the right. As soon the cursor is placed on the “Special Features,” Dr. Z’s Corner will welcome them in no time with its debut issue published in June 2014.

This holiday season, as we reflect on 2015, I would also like to congratulate the students from all engineering schools in the metro area. This includes UDC, Howard, UM-College Park, George Mason, Catholic, Morgan State, Virginia Tech, and Villanova, who read our column, downloaded hundreds of problems from this site for free, tirelessly attended our pro-bono Saturday classes and finally “conquered” the FE and PE exams. We have to add; some of our readers were not as fortunate and could not make it on their first attempts. Still, they have graciously sent us thank-you notes as well. I will never forget the note that I received from an engineering student from CUA who not only diligently attended to our Saturday classes, but also brought several students with her from her school week after week. She wrote:

Dear Dr. Z,

I hope all is well with you. With finals approaching and the semester almost over, I won’t be able to stop by your Saturday classes before the year ends. Although I did not receive your email, my friend told me that you have sent us an email asking about the FE exam results. Unfortunately, I was not able to pass the FE exam… I apologize Dr. Z., for letting you down! I know that you had faith that I will pass…. However, my goal is still to pass the exam before I graduate this coming May, so I’m planning on retaking the exam probably on February. I will be working on the problems on Dr. Z’s Corner during the holiday break. Despite failing, I would want to thank you for all your help in our preparation for the exam. I also look forward in going to your Saturday Classes, if you still have them early next year. Sincerely

I want this outstanding engineering student to know that she did not let Dr. Z. down at all. Just the contrary, considering her full-time work to support herself and pay her bills, her course work to finish and the finals, she did remarkably well on her first try. I am confident; we will support her and she will pass her exam in February. Our promise has always been “we’ll never rest our case, until all our students who read Dr.Z’s Corner and attend our pro-bono Saturday sessions conquer their FE & PE exams.” For this month’s problems click here.

Finally, I want to wish each of you a joyous holiday season with peace & cheer in the New Year!

Until next time,

Ahmet Zeytinci, P.E., (Dr. Z.)
This email address is being protected from spambots. You need JavaScript enabled to view it.

Relevant Articles