- Determining the load on the beam using the tributary width assumption.
- Determining the maximum shear and moment by calculating reactions and drawing shear and moment diagrams.
- Calculating required cross section area and section modulus using the allowable stress criteria.
- Identifying the shallowest standard section that has both adequate area and section modulus.
- Calculation of the load on the rod.
- Calculation of the rods stress, then strain, then elongation.
- These calculations may be combined through algebraic manipulation.

- Determine the weakest of strong axis, weak axis, and crushing modes (this may be done either as an allowable stress, or as a load).
- Compare the weakest of those three to the actual stress (or load) in the column.
- If the actual is less than the smallest allowable, then column meets the criteria, otherwise it does not.

Arch 324, Introduction to Structural Design, University of Virginia

Last updated Friday, April 19, 1996, at 1:56 PM Copyright © 1996, Kirk Martini

Here is a good solution:

Here is a very clear solution to the problem.

In the above solution, the student appears to have realized the solution right away, and moved in a straight line toward an answer. The solution below, also correct, shows the more of the thought process in seeking a solution. The problem begins by writing out the deflection formula for a beam, but gives up on that approach since there is not enough information. The solution then writes out the basic definitions of stress, strain, and E-modulus, and manipulates them until the target unknown (deflection) is on one side of the equation, and the unknown quantities are on the other. This is a good example of problem solving "on the fly", a very important skill.

The key elements of a good answer are:

(Note that the sign convention for the moment diagram is not correct; it should indicate the sense of bending rather than a specific direction)

A correct solution to part g requires the following steps:

The solution above correctly calculates the allowable stresses for strong axis, weak axis, and crushing, but then compares them to each other, rather than to the actual stress; many people did this. The summary on the cover sheet outlines the general requirements.

The solution below correctly checks the criteria, although the notation used is slightly different from that presented in class. The allowable stresses are boxed, and the actual stress is circled.

The key idea is that the form of the serpentine wall gives it greater effective depth (moment of inertia, section modulus, spreadoutness) to resist lateral loads.

**4 b)**

The shear diagram is useful for two things: to identify areas where the shear is high, and in determining the sense of the shear, which tells the direction of the cracking. This solution explains it very well.

**4 c)**

The key words are eccentricity and moment. Many people answered the question in terms of internal force releases, such as expansion joints. That issue is unrelated to the techniques of using double and single connectors and members.

**4 d)**

This a matter of basic definitions. Some people said that pre- and post- related to issues of before and after construction and assembly, but it relates only to the distinction of whether tendons are tensioned before or after concrete hardening.

**4 e)**

The two basic reasons are the control of cracking and deflections, and either one was accepted. Several people responded that pre-stressing was done to increase strength or load carrying ability, which is not

Last updated Friday, April 19, 1996, at 1:56 PM

Copyright © 1996, Kirk Martini

Please send comments or questions to Martini@virginia.edu