Please I need Help! Write a computer program to calculate the moment-curvature (
ID: 3889100 • Letter: P
Question
Please I need Help!
Write a computer program to calculate the moment-curvature
(M-) relationship for an arbitrary steel section having one axis of symmetry
perpendicular to the axis of bending. The general cross-sections to consider
are limited to those which can be built by the addition of rectangular sections
having parallel baselines (i.e., the user of the program should only need to
input data for three rectangles to define a W-shape).
This moment-curvature analysis is to be accomplished by subdividing the
final section created into a high number of layers (the program should use a
default of 100 layers, but also allow the user to specify this number, up to a
maximum of 10,000 layers). Only flexure needs be considered (i.e., neglect the
effect of axial, shear, or torsion forces). An elasto-perfectly plastic steel model
is to be used.
Incremental loading up to 98% Mp is to be considered in generating the
moment-curvature curve. The program should allow the print out of the stress
values at all layers, if required.
It is highly recommended that each well identified task be assigned to a
separate subroutine. Following are suggested subroutines which may be useful
in the program architecture. Write and test each subroutine individually for
efficient programming.
* Input and assembly of total cross-section. For example, a T section
would be defined by only two rectangles.
* Automate layering, subdividing into the number of specified layers.
* Initialize stress values for all layers, and set initial parameters.
* Create environment for iteration strategy.
* Increment curvature tentatively by a given step.
* Increment Stresses for all layers per steel behavior model.
* Calculate the resulting moment by summing contributions from all
layers.
* Calculate the resulting axial force by summing contributions from all
layers.
* Guess location of neutral axis at a given step, and adjust the guess
through iteration depending on the previous results.
* Determine of convergence is reached according to a selected tolerance
on the axial force (maybe as a fraction of y versus resulting P/A).
* Accept converged result and move on to additional curvature step.
Print M and values for that step. Print stresses at all layers, if
required.
Check the program using the cross-sections for some of the other above
problems. In particular, present the resulting M- curve for a T-section built
of two steel plates (flange is 6 x 0.75 in and web is 9 x 0.75 in) as well as stressdiagram
at two intermediate points between My and Mp.
Comment on what changes would be necessary to:
1. Modify the program such that the cyclic behavior can be considered
2. Consider bi axial bending.
3. Include non-null axial force.
4. Include general nonsymmetric cross-sectional shapes.
Submit source code, compiled executable, input and output files of verification
problems. Use comment-lines generously in the source code, identifying
clearly purpose of subroutine and definition of all variables used. Any programming
language can be used.
Explanation / Answer
Structural design of reinforced concrete structures is an iterative process. It begins with the layout of the structure or, in other words, with the selection of the structural system. Any practitioner will admit that this initial step is by far the hardest part of the process. It requires the designer to come up with a synthesized whole for the building, laying out all the component elements (columns, girders, beams (or joists), and slabs). Furthermore, the designer must also estimate the sizes of the elements within the space in order to go to the next step, that is, to analysis. The flowchart of Figure 2.1 presents a somewhat simplified picture of the process. Oddly enough, it begins with a step in synthesis, or the conception of the structure. This step is nonmathematical, for the aim of the study at this point is to look at what the building structure should do. What spaces are required? What is the minimum column spacing required to fit the architectural program? But before we reach the part designated as “Analysis” or “Design,” we must complete another exercise: identifying the loads that the structure may be subjected to in its life span.