A Neural Network Model for Shear of RC Beams

Experiments have shown that as the depth of the beam increases, the intensity of shear stress decreases especially in lightly reinforced beams. This phenomenon is referred to as “size effect”. Shear strength is not constant as given by some design codes like the ACI. To understand size effect, an artificial neural network (ANN) model was developed for RC beams without stirrups which fail under diagonal tension.

The ANN model consists of five input nodes representing (1) the compressive strength of concrete, f’c, (2) beam width, b, (3) effective beam depth, d, (4) shear span to depth ratio, a/d, and (5) longitudinal steel ratio. The output is the shear stress, Vu/bd. The graphical user interface of the Visual Basic program of the ANN model is shown.

The figure shows the simulation where the depth (d) was varied from 20 cm to 100 cm for two values of f’c and a/d and constant values for b at 15 cm and r at 2.75%. The size effect is obvious where the shear stress decreases with increasing depth. The experimental results by Kani shows a similar trend as the model. The shear stress also depends on the shear span to depth ratio – a shorter beam (a/d = 2.5) has a larger shear strength than a longer beam (a/d = 5.0).

How safe our our large RC beams with respect to shear failure? Structural engineers must take note of the decrease in shear strength of concrete for large beams so that they can provide adequate shear reinforcements or stirrups.

Reference: Oreta, A.W.C. (2004). "Simulating size effect on shear strength of RC beams without stirrups using neural networks." Eng'g Structures 26(2004) 681-691, Elsevier.

Visual Basic Games in Civil Engineering

In the laboratory course on Computer Methods in Civil Engineering at DLSU-Manila, aside from computer applications in civil engineering, I required the students to create game applications related to civil engineering. The randon number generator function is a very useful function in game simulations. These game applications may be used to review the students on their understanding of the concepts and equations in civil engineering. Student competitions may be conducted using the software to make the class more interesting and enjoyable. Through these activities, the students’ understanding and retention of the concepts hopefully may be improved. Here are the GUI's of some of the game applications created by the students.

Hangeneering by J.P. Sy and D. Baluyot. Based on the game, "Hangman", this is a game to test the student’s mastery on solving reactions in statically determinate beams. There is a time limit which varies from 30 seconds to 90 seconds depending on the level of difficulty. The program chooses randomly the figure and the beam parameters. There is a formula for getting the score of the player. The game will be over when the user answered incorrectly three times or when the time has run out. This game can be played in the Engineering Mechanics (Statics) or Strength of Materials class.

Jeopardeng by C. Fabie and R. Masa: This is an adaptation of the famous American game Jeopardy. The game has four different categories that cover various topics about civil engineering. Each category has four objective questions. There is a data base of questions which are selected randomly. The user answers all questions under the four categories in any order, aiming to bag a high score. After all questions have been answered within the time limit, the user is prompted to the “Final JeopardENG Round”; wherein a computational question will be asked to the user worth 5000 points.

This game can be played in class to review the students about civil engineering terms, concepts and definitions. A competition among students can be done with the student having the highest score declared as the winner.

You may play some games at http://mysite.dlsu.edu.ph/faculty/oretaa.

Visual Basic Applications in Civil Engineering

Innovative approaches in teaching can be introduced in the classroom using the computer. In the author’s laboratory class on Computer Methods in Civil Engineering, students develop simple computer software applications and computer-based games on topics related to civil engineering using Visual Basic. By creating their own software applications, the students demonstrate their creativity and integrate concepts, methods and skills in mathematics, basic engineering and specialized civil engineering subjects. These software applications and games can be introduced in the classroom to motivate learning and to facilitate retention and understanding of engineering concepts. Here are examples of the Graphical User's Interface of the students' projects.

Beam Deflection Application: This is a software application for solving the elastic deflection and slope of a beam. The inputs to the program are the cross-section dimension and properties of the I-section and the beam loadings and lengths. The outputs include the moment of inertia of the I-section, the beam deflection and slope at specified point X from the left end. This application may be used in the course on Mechanics of Materials or Structural Analysis to demonstrate the effect of section properties, beam loading and lengths on the elastic deflection and slope of a beam. By computing the deflection of the beam at different values of X, the shape of the elastic curve can be drawn.

Open Channel Flow: This software application determines the normal depth of an open channel using Manning’s Equation. In this program, the user first selects the shape of the cross-section: (a ) rectangle, (b) trapezoid, or (c) triangle. The system of units have to be chosen also. The inputs to the program are the dimensions of the cross-section and Manning equation parameters, S, n and Q. The output of the program is the normal depth of flow. This software application can be used in the courses, Fluid Mechanics or Hydraulics. The values of the various parameters, such as dimensions of the cross-section, slope of channel bed, coefficient of roughness or flow rate, maybe varied to study the effect on the normal depth of flow.

You may download and try these programs at my website at http://mysite.dlsu.edu.ph/faculty/oretaa.

GRASP Analysis of the Top 3 Popsicle Stick Bridges

In the strength category of the 5th DLSU-CES Bridge Building Competition, the bridges with weight W were subjected to two-point loads using a UTM (Read the blog on bridge testing). The values of P and D at failure were noted to get the Strength rating S=P/(D*W). The bridge with the largest S wins the competition.

The value of S depends on the stiffness (P/D) of the bridge and the weight W. The competition measures how efficient the materials were used to obtain a structure with large ratio of stiffness to weight.

Using the GRASP software, the top 3 winning bridges (B13, B03 and B06) in the strength category were analyzed . Observe the very interesting deflected shapes of the models. The figure also shows the members with axial tensile forces (labeled T). Why did the top bridges perform better than the others? What are the factors that contributed to the large stiffness (P/D) of the bridges? One major factor is the material property of popsicle sticks - the tensile stress capacity is larger than the compressive stress capacity in popsicle sticks. It would be easier to break the popsicle stick due to compression than to tear it due to tension. Hence, if you want to efficiently use the strength of popsicle sticks, design your bridge such that tensile forces not compressive forces are developed in most of the members. In the top 2 bridges - B13 and B03 - relatively large tensile forces were induced in the diagonal members compared to the compressive members.

Another factor is buckling failure in the compression members. If you want to increase the capacity of the members against buckling, then provide braces. The top 2 bridges have horizontal braces at the top and bottom preventing lateral buckling of the members. Bridge B06 which is 3rd in the competition has relatively larger compressive forces in the top chord and diagonal web members. Observe the buckling failure of the top chord. If only horizontal braces were installed at the top, the bridge may have developed a larger capacity and less deflection before failure.

Another factor which increased the stiffness of the bridges, particularly the top 2 bridges is the use of a deep box girder. This results to a relatively light-weight bridge but effective against bending. Sticking together popsicle sticks forming stiff griders like in the bridges shown result to very heavy and not very efficient bridges. They may carry a larger load (P) before failure but the ratio with weight may be smaller because of the large bridge weight.

Modeling your bridges and analyzing them using a software like GRASP before the actual construction will guide you on how to improve the bridge designs. You can redesign the arrangement of the truss members, increase the depth or know the location of braces to prevent buckling failure.

Understanding 2D Structural Analysis

In my computer laboratory class on "Structural Engineering Computer Methods", the students use Structural Analysis software like GRASP, ETABS and SAP2000. Learning to use the software is not the end itself but learning concepts on structural analysis is the primary objective of the course. To achive this objective, I wrote "Understanding 2D Structural Analysis" - an exploratory-type of instructional and learning material consisting of ten modules about modeling and analysis of framed structures in 2D using GRASP. Each module focuses on a specific issue on structural modeling and analysis which is discussed with the aid of graphical and tabular results obtained from GRASP. The set of learning modules is not a substitute to a textbook on structural analysis. The theory is not presented. No derivations or equations can be found. The student or reader must refer to the textbooks for definitions, equations and techniques. Each chapter begins with background information and a “case study”. The reader explores the issues raised in the case study through the “Things to Do” GRASP activities or by simply observing and analyzing the “Observation” and graphical and tabular results presented in the module. Included in the modules are “Things to Try” GRASP exercises and “Things to Ponder” comments on the analysis and design of structures. Using the set of learning modules, the reader or student with the aid of GRASP discovers important insights on the response and behavior of structures due to variations in the parameters of the model and configurations of the structure, changes in member and material properties, and also changes in the restraint and loading conditions. Through the graphical results, the student can visualize the phenomena and this would accelerate his understanding of concepts through the experience of seeing and interpreting solutions to various structural modeling and analysis problems. You may download this book from my website and use it in your class.

Structural Analysis Tips to Popsicle Stick Bridge Builders (Load Application)

Using a structural analysis software like Graphical Rapid Analysis of Structures Program (GRASP ) developed by the Asian Center for Computations and Software (ACECOMS) can help popsicle stick bridge builders in designing their bridges. The behaviour of bridges depends on how and where the loads will be applied. For example, if two concentrated loads will be applied to test a bridge with a truss design, applying the load as shown in the figure at the bottom or uppr part of the bridge will make a lot of a difference. The GRASP software was used to compare the maximum deflection at the bottom horizontal elements of the two bridges. The structures were analyzed as a "frame" since the joints may be assumed rigid because of the glued connections. The deflection for Bridge 1 where the loads were applied at the bottom is 20% higher than Bridge 2 where the loads are applied at the top. For Bridge 1, the bottom horizontal elements have large bending moments and axial forces and diagonal truss members carry large axial forces - the top horizontal members had minimal stresses. For Bridge 2, on the otherhand, the top horizontal elements may have large bending moments but the axial forces are not so large compared to bridge 1. The bottom horizontal elements now contributed more in resisting the loads by carrying more axial forces as compared to bridge 1. The diagonal truss elements of bridge 2 carry almost the same magnitude of axial forces. So before designing your bridges, know how and where the loads will be applied. It will make a lot of a difference in the bridge performance!