Crippling is a phenomenon associated with local loading of high intensity perpendicular to the plane of the web. It is most evident in the case of concentrated loading (Figure 17) or at intermediate supports of continuous beams. It is often more severe than web buckling, since crippling reduces the effective depth of a section and there is no post-critical strength. Depending on the webs' eccentricity relative to the load direction, and on the category of loads (see below), various values for web crippling resistance can be expected (Figure 18)

http://www.fgg.uni-lj.si/kmk/esdep/master/wg09/l0100.htm

Web crippling is actually local buckling that occurs when the web is slender (i.e. h/tw is large).  Figure 8.5.2.1 is a rough illustration of the behavior being considered.  The behavior is more restrained when the point load is applied away from the ends of the member, consequently there are separate equations for when a concentrated transverse load is locate near or away from the end of the member.

This limit state is to be checked at each location where a concentrated force is applied transverse to the axis of a member.

The Limit State

SCM specification J10.3 covers web crippling due to concentrated point loads applied to the flange.

The basic limit state follows the standard form.  The statement of the limit states and the associated reduction factor and factor of safety are given here:

LRFD ASD

Ru < Rn Ra < Rn/

Req'd Rn = Ru / < Rn Req'd Rn = Ra  < Rn

Ru / (Rn)  < 1.00 Ra / (Rn/) < 1.00

= 0.75 = 2.00

[2010 Spec note:  The variable 'N' in the 2005 Specification has been replaced with 'lb' in the 2010 Specification.]

The values of Ru and Ra are the LRFD and ASD factored loads, respectively, applied to the beam. 

In this case Rn is the nominal web crippling strength of the member is computed using SCM equations J10-4 and J10-5.

The two equations are needed to account for the difference in available web material between the web at the end of the beam and the web away from the end of the beam.  The same principle was discussed in the section on web yielding.

Equation J10-4 (see SCM specification J10.3) applies when the applied force is not near the ends of the member.  It is a buckling equation and has numerous terms.

Equations J10-5 apply at the ends of the member.  The two equations are slightly different and depend on the ratio of bearing length to overall depth of the beam.

Sample Spreadsheet Calculation

The given spreadsheet example computes the reaction capacity, Rn, as controlled by web crippling for a typical W section. The input values are in the grey shaded cells and the results in the yellow highlighted cells.

http://www.bgstructuralengineering.com/BGSCM14/BGSCM006/index.htm

http://www.bgstructuralengineering.com/BGSCM14/BGSCM006/BGSCM00602.htm

http://www.bgstructuralengineering.com/BGSCM14/BGSCM006/BGSCM00603.htm

http://www.nptel.iitm.ac.in/courses/Webcourse-contents/IIT-ROORKEE/strength%20of%20materials/lects%20&%20picts/image/lect37/lecture37.htm

Design Considerations

In practice, for a given material, the allowable stress in a compression member depends on the slenderness ratio Leff / r and can be divided into three regions: short, intermediate, and long.

Short columns are dominated by the strength limit of the material. Intermediate columns are bounded by the inelastic limit of the member. Finally, long columns are bounded by the elastic limit (i.e. Euler's formula). These three regions are depicted on the stress/slenderness graph below,

The short/intermediate/long classification of columns depends on both the geometry (slenderness ratio) and the material properties (Young's modulus and yield strength). Some common materials used for columns are listed below:

Material Short Column Intermediate Column Long Column

(Strength Limit)(Inelastic Stability

Limit)(Elastic Stability Limit)

Slenderness Ratio ( SR = Leff / r)

Structural Steel SR < 40 40 < SR < 150 SR > 150

Aluminum Alloy AA   6061 - T6

SR < 9.5 9.5 < SR < 66 SR > 66

Aluminum Alloy AA   2014 - T6

SR < 12 12 < SR < 55 SR > 55

Wood SR < 11 11 < SR < (18 ~ 30) (18 ~ 30) < SR < 50

 In the table, Leff is the effective length of the column, and r is the radius of gyration of the

cross-sectional area, defined as .

Radii of gyration for standard beams, common beams, and other common areas can be found in the geometry section.

Transition Zone For long columns (large s), the Euler Buckling Strength reduces rapidly. For very short columns (small s) the Buckling Strength is large. However, the Column's Strength cannot exceed the Compressive Strength of the material, SC. Thus, depending on the Slenderness Ratio, a column fails by either:

(1) Material Failure (e.g., yielding in metals) or (2) Geometric Instability (buckling)

A transition point between yielding and buckling can be determined by setting the buckling strength equal to the yield strength: cr = SY. The Transition Slenderness Ratio is then:

str = E

SY

1/2

In reality, a "sudden change" from one type of failure mechanism to another. Columns of Intermediate Length are governed by equations which provide a transtion between Yielding and Buckling. Steel, Aluminum and Wood each have unique transitional equations.

Critical Stress vs. Slenderness Ratio

Crippling Failure

Crippling is a phenomenon that occurs in a member that is under compression with sufficiently short length to prevent instability. Unstable members under compression tend to buckle as shown in figure below.

I will go over buckling some other time, but the key point to remember here is that a long member doesn’t have the lateral stability for crippling to occur because the long member will fail under buckling before crippling. Stability in aircraft are genrally provided by web and

skin members. As  compressive force increases, these mating members will tend to hold the statbility of the main load carrying part. Hence allowing the part to reach crippling. For example look at the sketch below. 

In the first sketch the compressive load is evenly distributed across the entire section of the plate. As the compressive load is increase the plate will buckle and it won’t be efficient is carrying load. As I like to say “ the load is not stupid”, if the plate can nolonger carry load it will try to look for an alternative path. As you can see in Sketch 2, the load runs to the stiffer side supported by the I beams. Failure of this structure will occur when the supported sides reaches compressive yield strength of the material. This yield strength can be think of as the crippling strength.

Using the same thinking, an L angle as shown below can have it’s flanges buckle as the compressive load increases. As the compressive load further increase the load will “run” to the stiffer corner of the L-angle. Further increase in load will cause the L-angle to fail  under what we call crippling. This brings us to another key point about crippling, the crippling allowable is a function of the structures geometry. Generally, the more corner a section has, the higher the crippling allowable. For example an U-section will have an higher L-section crippling allowable as I will prove later on in another post. This post was just intended to give you an overview of what crippling is and I hope it did the job. If you have any comments, questions or correction please leave me a comment. Stay tuned for the hardcore calculations on crippling soon.