analysis and design of members for axial compression

Compression members are structural elements that are subjected only to axial compressive forces; that is, the loads are applied along a longitudinal axis through the centroid of the member cross section, and the stress can be taken as f = P/A, where f is considered to be uniform over the entire cross section.The most common type of compression member occurring in buildings and bridges is the column, a vertical member whose primary function is to support vertical loads. In many instances, these members are also subjected to bending, and in these cases, the member is a beam–column.

compression limit state

For doubly symmetric compact and noncompact compression members, flexural buckling is normally the governing limit state. An ideal pin-ended column with an applied axial load causing flexural buckling in the elastic range, fails at a critical stress given by the Euler expression as shown in the left where L is length of column and r is radius of gyration.
The Euler expression may be modified by using the factor K =, an effective length factor where KL/r is the slenderness ratio.

Here are the steps that must be followed in order to design compression members correctly.

1. Check the slenderness ratio. Slenderness limitation = 200.

2. Check if the section is non-slender (compact/non-compact) or slender. Refer to NSCP 2015 SECTION 502.4.

3. Calculate the nominal compressive strength, Pn. Refer to NSCP 2015 SECTION 505.3 and 505.4 for non-slender section, and SECTION 505.7 for slender section of doubly symmetric I-shaped members.

4. Calculate the allowable compressive strength (ASD) and design compressive strength (LRFD) of compression members.

5. Check the demand-capacity ratio (DCR). DCR ≤ 1.00

effective length

The effective length factor K converts the actual column length L to an equivalent pin-ended column of length KL. The factor accounts for the influence of restraint conditions on the behavior of the column and KL represents the length over which the column actually buckles.
There are two methods that can be used in determining the effective length factor. These are:

Tabulated factors for stand-alone columns with well-defined support conditions.
Alignment charts for columns in a rigid framed structure.

NOMINAL COMPRESSIVE STRENGTH

The design compressive strength and allowable compressive strength can be obtained by multiplying the nominal compressive strength by the resistance factor for LRFD or dividing it by load factors for ASD).
However, it should be noted that nominal compressive strength refers to the lowest value obtained from applicable limit states of flexural buckling, torsional buckling, and flexural torsional buckling.
The figure shown on the left displays cross-sections of steel shapes and their corresponding limit states to be computed depending on if it has slender elements or not.
Shown below are the resistance and safety factors used for computing the design and allowable strength of members subjected to axial compression.

member properties

Sections subjected to axial compression may be classified as non-slender element or slender-element sections. For a non-slender-element section, the width-to-thickness ratios of its compression elements shall not exceed λr. If the width-to-thickness ratio of any compression element exceeds λr, the section is a slender-element section.
Unstiffened elements refers to elements supported along only one edge parallel to the direction of the compression force. On the other hand, stiffened elements are supported along two edges parallel to the direction of the compression force.
By checking the limiting width-thickness ratios, an engineer can determine if the section is a slender or a non-slender element. Shown in the right are the limiting width to thickness ratios of various elements.

flexural buckling of members without slender elements

Inelastic buckling governs when KL/r ≤ 4.71(E/Fy)^0.5 and Fy/Fe ≤ 2.25. The critical stress is obtained using the formula shown on the left.
Elastic buckling governs when KL/r > 4.71(E/Fy)^0.5 and Fy/Fe > 2.25. The critical stress is also shown.
It should be noted that the nominal compressive strength is given by the formula Pn=FcrAg, where Ag is the gross area of a member.
The design and allowable compressive strength can be obtained using the relations shown.

supplementary materials and recorded meetings

20221013- CENG131 Module 3.pdf

20221207- CENG131 Module 3b.pdf

rza-xojq-bkp (2022-12-12 19:06 GMT+8)

reflection

The module entailed the step-by-step procedure on how to solve for the design and allowable compressive strength of members subected to compression. After attending synchronous meetings and solving sample problems, I learned that the concept of using effective length factor K plays a very important role in compression member design. When K factor is multiplied by the actual length of the end-restrained column, for example, will give the length of an equivalent pin-ended column whose buckling load is also the same as those in the end-restrained column. Also, I have learned that when computing KL/r, it should not be greater than 200 for computing the critical load. Lastly, it is highly important to check first if the compression member is a slender or a non-slender element.

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