Do not repeat previous answerProblem 1 For flexure determine

Do not repeat previous answerProblem 1: For flexure, determine which HSS square sections (7 and deeper) are compact, non-compact, or slender (list slender ones and non-compact ones) if Fy 80 ksi considering the web and the flange. It would likely be helpful to use the b/t and h/t ratios provided in the tables.

Solution

if a W10 × 12, with a yield stress of 50 ksi, satisfies the compact section criteria.

The limiting slenderness parameter for the web of a rolled I-shape is given by AISC 360 Table B4.1b as



From AISC Manual Table 1-1, a W10 × 12 has a value of



The limiting slenderness parameter for the flange of a rolled I-shape is given by AISC 360 Table B4.1b as



From AISC Manual Table 1-1, a W10 × 12 has a value of



Hence a W10 × 12 with a yield stress of 50 ksi is not a compact section.

4.3.2. Noncompact Section

A noncompact section is one that can, prior to local buckling of the flange or web, develop a nominal flexural strengthMn given by



The criteria for determining noncompactness in the flange of rolled beams is defined in AISC 360 Table B4.1b as



where rf is limiting slenderness parameter for a noncompact flange.

The criteria for determining noncompactness in the web of rolled beams is defined in AISC 360 Table B4.1b as



where rw is limiting slenderness parameter for a noncompact web.

The nominal flexural strength of a section with compact web and noncompact flange with adequate lateral bracing, is given by AISC 360 Eq. (F3-1) as



where is bf/2tf = beam flange slenderness parameter.

Tabulated values of bMp and Mp/b, in AISC Manual Table 3-2 allow for any reduction because of noncompactness.

Example 4.5.:Noncompact Section

Determine the design flexural strength and allowable flexural strength of a W10 × 12, with a yield stress of 50 ksi.

From Example 4.4, the relevant slenderness parameters for a W10 × 12 are



From AISC 360 Table 1-1



The plastic moment of resistance is given by


From AISC 360 Table B4.1b, the limiting slenderness parameter for a noncompact flange is


From AISC 360 Eq. (F3-1), the nominal flexural strength is given by


LRFD

ASD

The design flexural strength is


The allowable flexural strength is


These values are given in AISC Manual Table 3-2 as bMp and Mp/b.

4.3.3. Slender Section

A slender section is one that cannot develop the yield stress prior to web or flange local buckling. In accordance with AISC 360 Sec. B4, a section is classified as slender when the slenderness ratio of the flange or web exceeds the limiting slenderness parameters for a noncompact section. For flange local buckling, a slender section is defined as


For web local buckling, a slender section is defined as


The nominal flexural strength of a section with slender flanges, with adequate lateral bracing, is given by AISC 360 Eq. (F3-2) as


where kc = 4/(h/tw)0.5

0.35

0.76

= bf/2tf

There are no rolled I-shapes with slender flanges or webs.