Lesson 16-24

The y-axis will always control the buckling strength of a W shape.

False. Either axis may control the buckling strength of a W shape.

Columns that buckle in the elastic region have higher design strengths than columns that buckling in the inelastic region of behavior. 

False. The inelastic region of buckling results in higher buckling capacity.

A reduction or resistance factor (phi) of 0.85 is used for compression members. 

False. Resistance Factor is 0.90

The column design tables for W shapes (Table 4-1) can be directly used for both axes of buckling (x- and y-axes).  

False. The table 4-1 can only be used for weak- or y-axis buckling

In the AISC Specification, local buckling modifies the buckling capacity of a column by reducing the gross area to account of the loss of cross section due to the local buckling of an cross sectional element. 

True. An effective area is calculated by reducing the gross area by the area of cross sectional element that buckles locally.

When determining the buckling capacity of a column that is susceptible to local buckling, a lower critical buckling stress, F_cr, is calculated.  

False. The critical buckling stress calculation remains the same. It is the cross sectional area that is reduced.

For columns, any cross sectional shape will have 3 possible global buckling modes (flexural, flexural-torsional, and torsional).

False. Which global buckling mode a column is susceptible to is based on the number of planes of symmetry the column has.  A column at most has 2 of the 3 possible global buckling modes.

Buckling about and buckling in a given axis means the same thing.  

False. The terms “in” and “about” refer to opposite axes.

Connector spacing in built-up columns affect the buckling capacity of both axes.  

False. The connector spacing only affects buckling strength about the axis coinciding with the connection plane.

Bending or flexure in a member is the result of axially applied loads. 

F. Bending or flexure is the result of transversely applied loading or applied end moments. 

Internal shear and moment are the result of transverse loads and applied moments acting on a beams.

T. As a result of transverse loads and or applied end moments, both shear and moment develop in a beam

The internal bending strength of a beam is defined by the couple that forms from the flexural stress distribution.

True. The resistance to the moments that develop due to the applied loads is the result of the flexural stress distribution that forms.  Integrating the stress over the cross sectional area it acts on, the equal and opposite forces form a couple or internal moment that resists the applied moments

The design moment capacity of a beam is defined by the stress distribution that exists at the time of failure.

T. The maximum moment capacity is defined by the couple that forms at the time of failure due to the bending stress distribution

The elastic region of bending assumes a non-linear stress-strain relationship.

F.  In the elastic region of bending, the stress distribution in linear and assumes a linear relationship between stress and strain (which is defined by the modulus of elasticity, E

First yielding occurs in a hot-rolled beam when the extreme fiber ending stress goes from zero to the yield strength of the steel as the beam is loaded.  

F. Due to residual stresses, the beam will yield early.

The plastic moment is defined by a stress state that is fully yielded.

T. The entire cross section is assumed to be yielded, either in tension or compression.

The plastic moment defines the maximum flexural capacity of a beam.  

T. At the plastic moment, the cross section is fully yielded and no additional moment capacity can be achieved.

Determine the ELASTIC Section Modulus (in³) for a rectangular cross section that is 6 inches wide by 14 inches deep.

196

Determine the PLASTIC Section Modulus (in³)for a rectangular cross section that is 6 inches wide by 14 inches deep.

294

Determine the PLASTIC Section Modulus (in³) for an I-shape member with 1” x 6” flanges and a ½” x 20” web.

2450

Like a column, a beam has 2 regions of behavior. 

F. Unlike a column, which will buckle before it can yield, the beam can fully yield in bending, providing a third region of behavior. 

Lateral torsional buckling occurs in a beam due to the instability of the tension flange. 

F. It is the instability of the compression flange that causes lateral torsional buckling.

A W-shaped cross section that is shorter and stockier has a higher resistance to lateral torsional buckling that a deeper, more slender cross section.  

T. The deeper and more slender a cross section is, the more susceptible the cross section is to lateral torsional buckling.

A cross section that is susceptible to local buckling is called a Compact Section

Compact Sections are sections that are not susceptible to local buckling.

Instability, such as lateral torsional buckling, web local buckling, or flange local buckling, can reduce the bending capacity of beam to a level below that defined by the plastic moment.  

T. The plastic moment, which defines the maximum bending strength of a beam, may be reduced by instability issues. 

A non-compact section is a beam whose stress distribution at the time of failure is all elastic.  

F. A slender section is the one with an all elastic stress distribution at the time of failure.  A non-compact section has an inelastic stress distribution at the time of failure

Beam moment capacities in the elastic region are generally larger in magnitude than in the inelastic region.  

F. The elastic region results in lower moment capacities.

Determine the design plastic moment of a W12x50 of A992 in kip-ft.

270. The design plastic moment is determined by multiplying the Z_x of this section (which is 71.9 in.³ from Table 1-1) by the yield stress (50 ksi) and then reduced by the reduction factor for flexure which is 0.9  This gives a design moment capacity of 270 kips.  Do not forget to divide by 12 to convert from kip-in to kip-ft.  This value can be verified in Table 3-2 (p. 3-26).

Determine the maximum unbraced length (ft.) of a W18x46 beam at which the plastic moment is still valid for its moment capacity.

4.56 Using Eq. (F2-5) with an r_y of 1.29 gives an L_p of 54.7 in. or 4.56 ft.   This value can be verified in Table 3-2 (p. 3-26).  Make sure to divide by 12 to convert from inches to feet.

Using Table 3-2, what is the limiting laterally unbraced length, in feet, for the limit state of inelastic lateral torsional buckling, L _r, for a W21x50 of A992 steel.

13.6 The correct value for L_r, of 13.6 ft. is taken from Table 3-2, p. 3-25. 

A constant moment along the unbraced length results in the lowest resistance to lateral torsional buckling.  

T. A constant moment along the entire unbraced length is the worst case for lateral torsional buckling.

The bending coefficient, C_b, decrease the moment capacity of a laterally unbraced beam due to a non-constant moment along the unbraced length.  

F. The bending coefficient INCREASES the moment capacity of a laterally unbraced beam to account for a non-constant or linearly varying moment along the unbraced length. 

Double curvature in a beam will reduces the possibility of lateral torsional buckling.  

T. Double curvature reduces the possibility of lateral torsional buckling since the compression flange length is split between the top and bottom flanges.

When calculating the bending coefficient, C_b, using Eq. F1-1 only absolute values of the moments are used.  

T. Only absolute values of the moment are used in Eq. (F1-1).

When calculating the bending coefficient, C_b, the maximum moment may be located anywhere all the unbraced length

T

Using Table 3-1, determine the bending coefficient, C_b, for a simply supported beam with a uniformly distributed loading with lateral bracing at the ends and at mid-span.

1.3 The correct value is 1.30.  Make sure you understand how to use Table 3-1. 

The use of the bending coefficient, C_b, can result in design moment capacities that exceed the plastic moment of the section and are therefore invalid. 

T. The formulas used to calculate the design moment capacities in both the inelastic (F2-2) and elastic (F2-4) region of beam can return values that are higher in magnitude than the plastic moment.

The beam design plots (Table 3-10) provide the response curves for all W shapes commonly used as beams.  

T. The beam design plots are response curves for every W shape that is practical for a beam and are plotted using the governing design equations. 

When using the beam design plots, the lightest valid section for a given combination of required moment capacity and unbraced length is the first line to the right and above the intersection point.  

F. The beam design plots are response curves for every W shape that is practical for a beam and are plotted using the governing design equations. 

Using the beam design plots with the equivalent moment (required moment divided by the C_b) provides the required design moment and correct beam size without any further checks.  

F. Because you are going into the beam design plots with an artificially low required moment capacity because C_b is greater than 1.0, you must check to make sure the selected beam has sufficient capacity for the actual moment.

The limits for local buckling are the same for both columns and beams.  

F. The limits are different because of the different stress conditions.  The limits column columns are given in Table B4.1a while the beam or flexure limits are given in Table B1.4b.

Shear occurs in a beam when the moment between two points is constant. 

F. Shear occurs when there is an imbalance of moment between two points in a beam. 

The shear in a steel I-shaped beam is resisted by the web (assuming strong (x-axis) bending).  

T. The web of a steel beam resists the shear as the web is aligned parallel with the shear force.

What is the magnitude of the resistance factor used in shear design?

1

Using Table 3-2, what is the design shear capacity for a W21x50 of A992 steel (kips)?

237 The correct value of 237 kips is taken from Table 3-2, p. 3-25.  

Shear controls the design of a beam when:

A) The span length is short

B) A concentrated load is close to a support

C) Both of the above

D) Neither of the above

C

Almost all W shaped are not susceptible to shear buckling.  

T. Only a handful of W shapes are prone to buckling.

A W shape bend only about its weak axis (y-y) is susceptible to lateral torsional buckling.  

F. There is too much resistance in the x-axis for there to be lateral torsional buckling when a W shape is bent about its weak axis. 

Web local yielding can be minimized by decreasing the bearing length.  

F. The resistance to web local yielding increases by increasing the bearing length

Concentrated loads, like those that occur at supports, can cause the web of a W shape to buckle or cripple.  

T

The resistance factors for web local yielding and web local crippling are the same.  

F. The resistance factors are different.  The resistance factor for web local yielding is equal to 1.0 while the resistance factor of web local crippling is 0.75.

Web stiffeners and web doubler plates can be used to increase the resistance of the web against web local yielding and web local crippling

T

Sidesway buckling can occur at any floor level in a building.  

F. Sidesway buckling only occurs at the top of a column or top story of a building where the top of the column can kick out sideways if not properly braced in the lateral direction

Deflection criteria is provided in AISC-15.  

F. AISC-15 does not provide deflection criteria.  One must use other codes or specifications such as the International Building Code.

When checking deflections in steel beams, unfactored live loads are normally used.  

T. Only unfactored live loads are normally used to determine the deflections of steel beams

Determine the maximum deflection, in inches, a steel beam is allowed to deflect if its span length is 20 ft.

Determine the maximum deflection, in inches, a steel beam is allowed to deflect if its span length is 20 ft.

A beam or a column will be subjected to different forces only one force type at a time.  

F. Multiple forces can act simultaneously on a member, such as bending and axial compression on a column. 

The numerator of the interaction equation is the required strength of the member while the denominator is available strength or capacity.  

T.

It is acceptable for the summation of an interaction equation to exceed 1.0.  

F. If the summation of an interaction equation exceeds 1.0, it indicates that the member does not have sufficient strength to resist simultaneous loading and must be redesigned.

A steel beam has a x-axis moment capacity of 400 kip-ft and a y-axis moment capacity of 50 kip-ft.  What is the maximum moment, in kip-ft, that can be applied about the x-axis is the y-axis is subjected to 20 kip-ft?

240 The correct value is 240 kip-ft.  It is found by re-arranging the equation given in Slide No. 9 of Lesson 24 and solving for M_rx.

A suitable design for biaxial bending lies outside the interaction diagram.

F. If the design lies outside the interaction diagram, it means the interaction equation sums to a value greater than 1.0 and the design is insufficient.

When designing for biaxial bending, it is always possible to match the ratio of the plastic section moduli to the ratio of the required moments.  

F. This statement is false since most W shapes have a limited plastic section modulus ratio range for a given depth. 

When the applied y-axis bending moment is relatively large when compared to the applied x-axis bending moment, a short stocky cross section will be the most efficient.  

T. The ratio of the plastic section moduli of a short, stocky cross section matches more closely the ratio of the applied moments.

When designing a beam for combined bending and axial tension, it is best to start with the assumption that Eq. (H1-1a) will control.  

T. Since the Eq. (H1-1a) applies when the ratio of the required axial strength to that of the axial design strength is 0.20 or greater, the probability of this equation controlling the design is greater than Eq. (H-1b) controlling the design.