# 6-Definition of the effective area for tension members.

## Definition of the effective area for tension members.

### Effective area and shear lag factor.

The failure load is less than would be predicted by the product of An*Fult.
The shape as shown in the sketch is an angle under force and has bolts at the lower leg. P is a tension force.
The shaded area is stressed very little, which means that most of the stresses occur at the bolts located at the lower leg. and connected to the plate.

As the load is applied, the transfer of that load to the unbolted portion, will not occur immediately but, after a lag, that is why this phenomenon is called shear lag.

The phenomena which this situation is generally attributed to what is called shear lag and is  Illustrated in Figure 2-9. Note that the angle is connected alone with only one leg and only one leg is connected to the plate. This leads to a concentration of stress along that leg and leaves a part of the unconnected leg part of the un-connected leg unstressed or stressed very little.

This means that stress for the connected portion will be increased, due to no sharing of the unconnected part and may exceed the Fy. The further we move out from the connection, the more uniform the stress becomes.
In the transition region, the shear transfer has lagged and the phenomenon is referred to as shear lag.

Investigators have found that one major of the effectiveness of a member such as an angle connected by one leg there are two factors the first one is x̅, and the second factor is the connection length L.

### Effect of x̅ and connection length on the shear lag factor.

Comparing two shapes as shown, shape a. For an equal angle and shape b with an unequal angle, where the fasteners exist on the long leg side, the observation is such that when the distance x̅ is smaller, then the effectiveness of the connection is getting better. The smaller value of x̅, the larger the effective areas of the member, and thus the larger the member’s strength.

The x̅ is closer since the bigger area has closer  CG, as known from statics. So the angle in shape b is more effective than in shape a. Shear lag affects both bolted and welded connections, therefore the effective net area concept is applied to both types of connections, then Ae=U *An, and also for welded connections.

Shear lag affects both bolted and welded connections, therefore the effective net area concept is applied to both types of connections, then Ae=U *An, and also for welded connections.

Where x̅ is the distance from the centroid of the connected area to the plane of the connection, and L is the length of the connection.

If the member has two symmetrical planes of connections, x̅ is measured from the centroid of the nearest one-half of the area.

In the case of a wide flange connected, with a plate to the upper and lower flanges.

The web area has no connection, because of symmetry, the wide flange section can be converted to two T sections, and hence estimate the CG distance, or x̅, for half of the area.

Additional approaches for calculating x̅ for different connections. Types are shown in the AISC manual on pages, 16-1-178. The different values of U value are based on the shapes and the dimensions.

Cases 7 and 8, serve as an alternative to case 2-where u=(1-xbar/L). Take the larger value. The shear lag factor minimum value can be found from the ratio between connected part / gross area, but not applicable to plates and closed shapes, refer to specifications.

The major difference between Table D3.1 in AISC-360-16 the Table D3.1-AiSC-360-2010 exists in item 4, where the elements for case 4 include plates& angles, and channels with welds at the heel, Tees, and W section where loads are transmitted thru longitudinal welds only. The U value equation was revised.

### Solved example 4-1, how to estimate shear lag factor for a single angle?

It is required to determine the shear lag factor U, the net area An, and the effective area Ae. we have an angle of 5x5x3/8 inch, with 4 bolts, connected to one plate from one side.

We want to estimate the value of U, bolts are given as 4, 3/4 bolts A325 N bolts, so hole dia=3/4+ 1/8, Diameter of the hole=3/8 inch. Our expression U=1- x̅/ L,  where x̅ is the distance perpendicular to the load, refer to the table then we get the area for angle 5x5x 3/8 inch, the area=3.65 inch2.

Check the CG distance, the C.G is in the y-direction, but it is referenced as  x̅   and is=1.37 inch, what about the L distance, it is= 3*3 inches is the length of the connection, so U=1-and is=1.37 inch/l=1-(1.37/9)=0.848.

This is the calculation for the U value, but if referring to table U=0.80.

For four or more fasteners as in the third case of the table as shown select the bigger value of the two values, which is =0.848, then we estimate the net area as per the usual method Anet=Ag- sum(d*t), dia is=7/8 inch.
We can get the y bar for the angle L5xL5x 3/8 from table 1-7. y bar. we can see that the y bar is parallel to the unconnected leg.
The net area Anet=Ag -Ag- sum(d*t), Ag =3.65 inch2, dia 7/8 and t=3/8 of the angle,  sum(d*t)=7/8*3/8, only one bolt hole to be deducted, to be deducted from 3.65 inch2.

The value is 3.32 inch 2, then A -effective=0.848*3.32=2.82 inch2, which was the first example of the effective area.

## Practice Quiz.

### #1. Determine the effective cross-sectional area of the C12x25 shown in figure P3-18. The holes are for 3/4 inch diameter bolts. Standard-size bolt holes are used.

This is not the correct answer.

This is the pdf file used in the expansion of this post.

A) Design strength for a given W section bolted at flanges, this is the topic of the next post, it is a direct application for cases 2 and 7 for shear lag factor. The next post-post 7- is A Solved problem for Design strength.

B) For the shear lag factor U value for a welded angle which is an application to case 2, please refer to post 8.

C) For a connected angle by bolts for one leg only, the value of U is governed by the maximum value between case 2 and case 8. Please refer to the first solved problem in post 9.

D) For a connected section by transverse weld only which is case 3, please refer to post-9A-Practice problem-transverse weld of a WT section.

E) For a connected section by longitudinal weld only which is case 4, please refer to post-9b-Practice problem-longitudinal weld of a plate section.

F) For a connected section by longitudinal weld only which is case 4, please refer to post-9C-Practice problem-longitudinal weld of a C section.

For the same angle welded, the value of U is governed by case 2, please refer to the second solved example in post 9.

Chapter 3 – Tension Members– A Beginner’s Guide to Structural Engineering is a great external resource.

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