Ch 1. Basics Multimedia Engineering Statics Problem Solving Units
 Chapter 1. Basics 2. Vectors 3. Forces 4. Moments 5. Rigid Bodies 6. Structures 7. Centroids/Inertia 8. Internal Loads 9. Friction 10. Work & Energy Appendix Basic Math Units Sections eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Kurt Gramoll ©Kurt Gramoll

STATICS - THEORY

Introduction

Example of beam in equilibrium when
forces are acting in multiple directions

Welcome to Statics. For most engineering students this will be your first serious engineering class. Like most engineering classes, Statics relies on previous courses (math and physics) and will be used in future courses that you will take.

Statics has all the basics of a regular engineering course, but is not too complex. The course revolves around just two equations,

ΣF = 0    and     ΣM = 0

Another way to think about these two main equations is that all forces (F) and moments (M) acting on a object must be in equilibrium. If this was not the case, then the object would move. In Statics it is assumed that nothing moves, but in Dynamics (the following course) this restriction is removed.

Before solving actual statics problems, units, solution methods and significant digits need to be discussed.

General Solution Procedure

Example problem solved
with solution steps

The study of Statics involves only a few basic concepts and equations. The difficulty in statics is learning how to apply the equations to complex and different situations.

In engineering, following a set procedure in solving problems saves time and decreases the number of errors. Generally, the following five steps will help solve problems in statics.

1. Read and understand the question(s).
a) Identify all given data.
b) Identify exactly what is being asked.
2. Make sketches and draw free-body diagrams.
3. Set up the problem and apply all relevant
equations.
4. Perform the calculations.
5. Check and review the answer.

Fundamental Concepts

As the name implies, Statics refers to the static equilibrium of all forces and moments acting on a body. This condition can be written in mathematical form as

 ΣF = 0 Forces ΣM = 0 Moments

While not all problems have both forces and moments in all three directions, both equations need to be satisfied in all three directions for the object to be in static equilibrium. Even though these two equations are simply, applying them to a particular structure can be difficult. Where are the forces, what are their directions, what is known, etc. become the main issues in the most Static problems.

Significant Digits

In most engineering problems, there will be numerous intermediate steps and results. When writing down these intermediate results, it is important to use enough digits to minimize rounding errors. However, if too many digits are used, it takes a long time to write out the equations, and errors are easily made in keeping track of all numerical values.

In general, numerical values can be rounded to four significant digits without loss of accuracy. Even using three digits is usually safe for most problems. However, round all numbers the same. If even one number is rounded to 2 significant digits and all the rest have four significant digits, the problem can still be off by a large amount (over 2%).

Please note, significant digits is not quite the same as the just rounding decimal places. Significant digits are applicable to numbers both large and small whether nor not they have decimals. The table below shows a number of examples that illustrate that all numbers can be rounded to a given number of significant digits.

Every number in the calculator should not be round just for the sake of rounding. Let the calculator keep all digits.

 ActualNumber Significant Digits 1 2 3 4 5234.4567 5000 5200 5230 5234 0.003452 0.003 0.0035 0.00345 0.003452 98.2384 100 98 98.2 98.24 23000 20000 23000 23000 23000 729.5 700 730 730 729.5 0.0239 0.02 0.024 0.0239 0.0239

Practice Homework and Test problems now available in the 'Eng Statics' mobile app
Includes over 500 problems with complete detailed solutions.
Available now at the Google Play Store and Apple App Store.