Applied Studies 240: Introduction to Structures

Part III: Beams

Project 8: How Beams Resist Bending

Learning Plan

1. Review the Learning Outcomes.
2. Read the Introduction.
3. Complete the Required Reading and explore the online resources.
4. Answer the Focus Questions.
5. Add materials as appropriate to your Personal Archive.
6. Complete Project 8. (Revisit the marking matrix.)
7. Submit Project 8 as part of Collection 3 when you have completed Projects 7, 8, and 9.

Learning Outcomes

After successfully completing this project, you will acquire proficiency in the following areas:

1. Ability to describe and explain resistance mechanisms of beams and the lattice pattern of flow forces;
2. Ability to calculate deflection in beams;
3. Ability to calculate bending stresses and web stresses in rectangular beams;
4. Ability to calculate the internal shear stresses in a beam that result from an applied transverse load;
5. Ability to calculate the internal flexural stresses and strains in a beam that result from an applied transverse load;
6. Ability to design simple beams by selecting the required section modulus to resist flexural stresses; and
7. Ability to design bays of wood framing.

Introduction

In this project, you will examine in more depth how beams resist bending. You will learn how to shape and size a beam in the context of the parallel flow of forces and you will apply this understanding to design your own floor deck.

Required Reading

• Chapter 17: How Beams Resist Bending in Form and Forces: Designing Efficient, Expressive Structures

Supplemental Reading

If you found this project of interest, you may want to read the following:

• Mattheck, Claus. (2004). Design in Nature: Learning from Trees. Dresden: Springer. Analyses of trees, bones, and other examples from nature are used to illustrate how stress and bending actions influence growth and strength.

Focus Questions

1. How are forces transferred in a beam and how can you shape them to be more efficient?
2. Why are beams inefficient yet are still used?
3. What are the different types of beams and trusses, and how are they designed to resist bending?
4. How can you size a beam to resist bending?

Evaluation

Your work will be evaluated using the marking matrix outlined in the Evaluation and Grading section of the Course Orientation.

Project Description

In this series of projects, you will design and shape beams by understanding how beams react to bending. Your work here will consist of three small projects:

1. Shaping a beam for parallel flow of forces using Worksheet 17
2. Assigning sizes to the members of a deck frame
3. Designing your own floor deck

Project 8a: Shaping a Beam for Parallel Flow of Forces

In Chapter 17, you learned that the prismatic or rectangular cross-section beam is inherently inefficient, and the flow patterns of the forces change from fan and parallel flow to lattice flow the more the beam gets shallower. The inefficiency of the beam results in most of its material being wasted. Using Worksheet 17, you will design a beam taking into consideration the parallel flow of forces. As you have seen in the design of a truss, it is possible to achieve much better relative efficiencies of volume of material, while being of the same depth and supporting the same load. (Note: There is an error on Worksheet 17 in the M, kip ft circles. The numbers -32 and -50 should each be moved one circle to the right.)

The assignment will guide you in the design of a uniformly loaded steel beam for the roof of a state fair pavilion, considering the longitudinal profile of the beam to match its bending moment diagram. Following the instructions on Worksheet 17, fill out the value of M and h in the table provided and sketch the shape of the beam that would be the most efficient in this situation.

Submit the table and the drawing of the beam in your collection.

Figure 8.1. This is an example of a uniformly loaded K-truss diagram showing a parallel flow of forces.

Project 8b: Assigning Sizes to the Members of a Deck Frame

On pages 475–482 in Form and Forces: Designing Efficient, Expressive Structures, you learned about architect Robert Dermody and his method of calculation to assign sizes to the members of a deck frame. Using the same method, answer Exercise 1 on page 489. For this project, you are requested to draw a floor plan of a child’s playhouse, and the framing plan for the floor, and find the required sizes of all the members of the frame.

Project 8c: Designing Your Own Floor Deck

For this project, you will need to use your own design project (see Identifying a Suitable Project). Using the same method as Project 8b, making assumptions of the loading that may take place in a room or floor of your building, design a floor deck using those dimensions and try to suggest reasonable structural members and sizes, using Fig. 17.25 on page 476.

Submit a sketch of your floor plan, a drawing of your framing plan, and the sizes of your structural members. Include an explanation of your reasoning and your calculations with your suggestion of size and member type for your floor deck.

Figure 8.2. Here is an example of what a deck frame drawing with the member sizes would look like.

Review Terms

You should be familiar with and able to define the following terms and concepts:

arm of internal forces
arm of resisting moment
bearing stress
bending moment
bending stress
depth of beam (d)
depth-to-span ratio
Gerber beam
K-truss
longitudinal stress
Michell beam
modified K-truss
moment of inertia (I)
neutral axis
neutral plane
principle of least work
resisting moment
section modulus (S)
self-weight
shear stress in beams
stress block
stress perpendicular to grain/parallel to grain
total longitudinal bending force (TF)
truss model
web stress
width of beam (b)

Submission Requirements

For Collection 3, include the following items from Project 8:

• Project 8a – Worksheet 17
• Project 8b – drawings and design values
• Project 8c – drawings and design values