# UTPA STEM/CBI Courses/Design of Steel Structures/Compression Members

Course Title: Design of Steel Structures
Lecture Topic: Compression Members
Instructor: Mohammad Azarbayejani
Institution:UTPA

## Backwards Design

Course Objectives
* Primary Objectives- By the next class period students will be able to:
** Understand buckling concept
** Calculate compression members capacity using LRFD and ASD
** Design compression members
* Sub Objectives- The objectives will require that students be able to:
** Differentiate between elastic and inelastic buckling
** Understand local buckling
** Calculate the effective length
* Difficulties- Students may have difficulty:
** Solving differential equations
** Remembering concepts from mechanics of materials class
* Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
** Design of columns that are vital elements for any building
** Design of any type of compression member such as compression members in bridge trusses
Model of Knowledge
* Concept Map
** Understand equations
** Put the ideas together
* Content Priorities
** Enduring Understanding
*** Calculate critical force and critical stress for columns with different boundary conditions
** Important to Do and Know
*** Difference between short and long columns and use correct code equations
*** If a member has a slender or non-slender cross section
** Worth Being Familiar with
*** Differential Equations
*** Mechanics of Materials
*** Structural Analysis
Assessment of Learning
* Formative Assessment
** In Class (groups)
*** Calculate the critical force for a cantilever beam
** Homework (individual)
*** Assigned from the textbook
* Summative Assessment
** First Midterm Exam

## Legacy Cycle

OBJECTIVE
By the next class period, students will be able to:
* Understand buckling concepts
* Calculate compression members capacity using LRFD and ASD
* Design compression members
The objectives will require that students be able to:
* Differentiate between elastic and inelastic buckling, local buckling
* Calculate the effective length
THE CHALLENGE
Grab a piece of wood and try to break the wood piece by applying tensile forces using your hands. Now that you know you can't break it, compress the wood by applying force with your palms at the ends of the piece of wood. Express your observations. Now grab a chunkier piece and compress it. Do you think the chunkier wood has more strength in tension or in compression? Can we make the wood so chunky that has the same strength in tension and compression? What other parameter is important in this experiment other than cross section? Can we make a steel member so thick and small that has the same capacity in tension and compression? What will be the failure capacity (in terms of stress) for tension and compression?
GENERATE IDEAS
The students will be asked to answer the challenge questions.
MULTIPLE PERSPECTIVES
The professor will lecture on buckling concept and elastic buckling for short columns and inelastic buckling for long columns so the students can have better understanding about the challenge questions.
RESEARCH & REVISE
The professor will derive the equation for the critical force of a simply supported column. Then, in groups, students will derive the equation for a cantilever column.
TEST YOUR METTLE
The professor gives feedback over the groups' results. The students are asked to do the homework over compression members which will be due at the beginning of the next class.
GO PUBLIC
Students will be given different compression member problems to solve during the first midterm exam.

## Pre-Lesson Quiz

1. What is the slenderness ratio?
* KL/I
* KL/r
* KL/EI
* KL/Er
2. Which column has a higher K?
* Cantilever column
* Simply supported column
* Both end fixed column
* One end fixed and one end pinned column
3. Which of the following sentences are true?
* Long columns have inelastic buckling problems.
* Long columns have elastic buckling problems.
* Short columns have more critical stress than long columns.
* Both b and c are correct.
4. What is the upper limit of the critical stress?
* Euler stress
* Yield stress
* Ultimate stress
* None of the above
5. Which part of an I-cross section is stiffened for local buckling?
* Flange
* Web
* Both the flange and the web
* Neither the flange nor the web

## Test Your Mettle Quiz

* Using LRFD, calculate the compressive strength of a both-ends-fixed column with a cross section of W14*74. The length of a column is 30 feet and it is made of A992 steel.
* Select a W 18*... cantilever column made of A992 steel to resist a dead load of 100 kips and a live load of 150 kips. The column is 10 feet high. (Use ASD method)