A Beginner's Guide to ACI 318-14

Chapter 3 - Strength Analysis

© 2018 T. Bartlett Quimby

Section 3.1

Basic Principles

Last Revised: 04/08/2018

The determination of cross sectional strength is based ultimate strength concepts. Ultimate strength is the absolute maximum strength of the section, sometimes called the failure strength. The computed ultimate strength of the section is called the nominal strength of the section. This strength is well outside the elastic range of the member. Adjustment factors are applied to both the nominal strength and the required strength to make them comparable in a design limit state.  The nature of the design limit equations is expressed mathematically by:

Required Strength(adjustment factors) < (adjustment factor) x (nominal sectional strength)

Required strength is a function of adjustment factors that will be addressed later. The intent of this chapter is to focus on the determination of the nominal member strength. In particular we will be examining the determination of nominal member strength of cross sections subject to axial and bending forces.

Strain Compatibility and Equilibrium

The nominal sectional strength on basic ultimate strength principles of mechanics with particular emphasis on Strain Compatibility and Equilibrium. as specified in ACI 318-14 22.2.

Strain compatibility refers to assumption that strains in both the steel and the concrete are proportional to their distance from the neutral axis and those strains are the same in adjacent steel and concrete. This is another way of saying that plane sections will remain plane--a basic assumption of mechanics. This assumption is critical to determining stress, and the resulting internal forces, acting normal to the cross sectional surface.

Equilibrium means that the sum of all forces on the cross section must equal zero.  These forces include the internal forces due to internal stresses and the overall axial and bending forces applied to the section which cause those stresses.

Ultimate Strength Condition

As previously mentioned, the ultimate strength of the member occurs when the section reaches the maximum forces that the member is capable of holding. This condition is defined by the Code assumptions regarding concrete strength. ACI 318-14 22.2.2.1 dictates that the maximum compressive strain in concrete, or the strain at which the concrete fails, is assumed to be 0.003.  This is value is consistent with test results and is an approximate value.

As a result of this assumption, we know that the strain is 0.003 at the extreme concrete compression fiber when ultimate strength is reached.  If we know where the neutral axis of the strain diagram is located then we can draw the strain diagram for the section.  Once we have the strain diagram, we can use stress-strain relationships to determine the internal stresses and forces resulting from the given strain condition. From there we can use equilibrium equations to determine the member forces (axial and bending) that would cause that particular strain condition to occur. These member forces are the nominal strengths of the member for that strain condition. This will become clearer as we work through the process.

The following sections walk through the process for determining the nominal strengths of a given section.  

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