Memento Mori

“In ancient Rome, when a victorious general paraded through the streets, legend has it that he was sometimes trailed by a servant whose job it was to repeat to him, “Memento mori”: Remember you will die. A reminder of mortality would help the hero keep things in perspective, instill some humility. “

- excerpted from “Steve Jobs” by Walter Isaacson, 2011.

Posted in Uncategorized | Leave a comment

Analytical Solution of Lateral Shear Stiffness of Single-Stepped Column

Bridge engineers must be familiar with the two lateral stiffness formulae for prismatic column sections; that is, k=3EI/L^3 for pin-fixed boundary condition and k=12EI/L^3 for fixed-fixed condition. These two simple formulae are fairly basic concepts often used in seismic analysis of bridge bents for ductility check and earthquake displacement assessment.

However, 3EI/L^3 or 12EI/L^3 is only applicable for prismatic columns. When column section varies along the height; for instance, a flared column or column supported by a large diameter drilled-shaft, we cannot directly use the two formulae any more. Luckily, nowadays finite-element programs like SAP2000 are popular so that you can simulate any section variations or boundary conditions you can imagine. But, sometimes computer-aid analysis may be even low-efficient than a quick hand-calc. For example, there is a bridge frame with 7 two-column bents all supported by Type-II drilled shafts to be built in a seismic zone, and we need verify the bent/column stiffness are compatible within the frame per Caltrans SDC (Seismic Design Criteria) article 7.1.1 balanced stiffness requirements. What shall we do if using SAP2000? Modeling every bent one-by-one and then push it to get lateral stiffness – good luck with that, you may spend half-a-day on finishing the modeling all 7 bents. In contrast to that half-day task, using the two equations shown in Appendix A and B below, you may just need one hour to get the work done.

As a verification of the two new formulae for single-stepped column, first assuming material and sectional properties E, I, and G are identical from top to toe, then the two complicated formulae are reduced to the simple form 3EI/L^3 or 12EI/L^3. Second, I created a SAP2000 model to perform case study and the SAP results match perfectly with what formulae generate. Please note that 3EI/L^3 or 12EI/L^3 only counts the flexural deformation of column, whereas SAP2000 will automatically consider both the flexural and shear deformations. Shear deformations can become significant in comparison with the flexural deformations when the column height is not significantly larger than the column sectional dimension (Priestley et al, §4.3.1, 1996).

[1] Priestley, M.J.N., Seible, F., and Calvi, G. M.. [1996]. “Seismic Design and Retrofit of Bridges”. John Wiley & Sons, Inc., New York, N.Y.
[2] Zhu, Boqin, Zhou, Jingou, and Xu, Zheming. [1993]. “Mechanics of Structures”. Tongji University Press, Shanghai, China.
[3] California Department of Transportation (Caltrans), Seismic Design Criteria, version 1.7, April 2013.



Posted in Uncategorized | Leave a comment

SAP2000/CSiBridge Bug#1

SAP2000 and CSiBridge are two well-known software that Computers and Structures, Inc. (CSI) develops in the past 30+ years. It aims at resolve finite element analysis problems mainly in the fields of Civil, Structural, and Mechanical Engineering. This series is to address a few bugs I came across when using CSI SAP2000/CSiBridge. Although these bugs are minor and hardly affect your works, I still want to write them down as a note for future reference.

————Let’s Get Started!———————

Bug#1, Incorrect Output of “Volumetric Ratio of Tranverse Confinement Steel” in Section Designer. 

Section Designer is a built-in sectional analysis tool shared by ETABS, SAP, and CSiBridge. With it, users can define a section more arbitrarily and one of its convenient features is to provide confined concrete property based on Mander’s equations that are adopted by Caltrans Seismic Design Criteria (SDC) and other codes.

The outputs that Section Designer provides for a Caltrans confined concrete section are all look good except the ρs, Volumetric ratio of transverse confinement steel to the concrete core.  Please be cautious if you intend to use this number for your subsequent calculation, as it is absolutely wrong. You may have to compute it by SDC equation (3.31).

Except that, I have not found any other error in Section Designer’s output for confined concrete section. And the erroneous output of ρs does not affect other parameters in Section Designer’s output. So it may only be a bug localized for some unknown reason.



1. Mander, JB; Priestley, MJN. “Observed Stress-Strain Behavior of Confined Concrete”, Journal of Structural Engineering, ASCE, Vol. 114, No. 8, Aug 1988, pp. 1827-1849.

2. Caltrans Seismic Design Criteria, version 1.6, Nov 2010.

Posted in Uncategorized | Leave a comment




Posted in Uncategorized | Leave a comment

test post

This is a test post…. test :)


Posted in Uncategorized | 1 Comment

Hello world!

Welcome to This is your first post. Edit or delete it and start blogging!

Posted in Uncategorized | 1 Comment

R Kelly – I Believe

                                I Believe — By R. KELLY
In small towns and big cities
We came together
As democrats, republicans, and independents
To stand up and say that we are
And our time for changed has COME..
When the mountain seems too high
And you don’t have the courage nor the strength to climb
And the road you’re on won’t end
But still you run though you cannot see the finish line
And dark clouds are over you
Your skies no longer blue
But you marched on straight ahead
Somehow you made it through
Got to the mountain peek
They left a path of me
Your victory made history and now
I believe, I believe, I believe
Oh, I believe, I believe, I believe… 

When it felt like you were weak
And couldn’t fight no more
On the ropes and it seemed like
You was gonna run out of breathe
When the world was on your shoulder
And the walls were in your way
You leaped and made it over
Through it all you kept the faith
With hope you set us free
You showed us how to dream
And now we can lift our voices
And forever sing
Now’s the time to look ahead
And thank our hero’s of the past
And celebrate this history
Let’s raise the flag cause
I believe, I believe, I believe
Oh, I believe, I believe, I believe
And when they tried to keep you down
You kept up your head
Never losing sight
You believed in what was right
You endured to the end
Walked through the strongest wind
The storm’s over
And a new day begins
And when our hope was dying
You brought us healing
And now I got something
To tell my children
I believe, I believe, I believe
Oh, I believe, I believe, I believe
Posted in Uncategorized | Leave a comment