Last Updated on February 14, 2026 by Maged kamel
- Solved problem 3-7 for staggered bolt-tension members.
- Brief description of problem 3-7 for staggered bolts.
- Investigate the first route abcf.
- Investigate the second route abcdf.
- Investigate the third route abcdeg.
- Investigate the fourth route acdeg
- Investigate the last route acdeg.
- What is the least net area for problem 3-7 for staggered bolts?
- LRFD and ASD design strengths.
Solved problem 3-7 for staggered bolt-tension members.
Brief description of problem 3-7 for staggered bolts.
We will review the solved problem 3-7 for staggered bolt-tension members. This problem is quoted from Prof. Segui’s handbook. The main aim is to investigate the different failure routes of failures and the corresponding net areas.
Prof. Segui has taken into consideration the actual force acting on each net area and adjusted the estimated net area, as we will see in the next calculations
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An angle of 6x8x1/2 has four bolt lines. Two lines are on the short leg, and the other two are on the long leg.
The bolt’s diameter is 7/8 inches, and the steel used is A36 steel. The LRFD and ASD design strengths for the same angle must be determined. For more clarity, please open the image in a separate link.
The image shows the arrangement of the bolt lines when the angle is unfolded to become a plate. The overall height of the unfolded plate is 13.50 inches. The height from the second and third grids is 4 3/4 inches.
The next slide image shows the different grids for the angle and spacing between bolts, and how we verify that the overall height matches the sum of the vertical distances between bolts.
The Force P is transferred through bolts to the other connected plate; each bolt will receive a portion of that load, equal to the total load divided by the number of bolts. We have ten bolts, so each bolt will transfer a value of P/10
Investigate the first route abcf.
The bolt’s diameter is 7/8 inches, and we will add an additional 1/8 inch to account for damage and bunching. The hole diameter will be equal to 1 inch.
The area of the unequal angle 6x8x1/2 is equal to 6.80 inches, obtained from the table of angles, and that area will be set equal to the gross area of the angle.
For route abcf, the gross area is reduced by two hole areas, totalling 1.0 inch2, with no staggered distances.
The net area can be estimated as (6.80 – 1.00) = 5.80 in^2. There is no bolt on the right side of the section; the section carries 100% of the load P.
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Investigate the second route abcdf.
For route abcdf, the gross area is reduced by three hole areas, totalling 1.50 in^2; there are two staggered distances. We will add the term S^2/4g*t to account for the additional area. The s distance is 1.50 inches, and we have two different g values: the first g is 2.50 inches, and the second g is 4.75 inches. The sum of S^2/4g*t equals 0.349 inch2. The net area of that route equals 6.8-1.50+0.349=5.649 inch2
The route’s net area is not adjusted because the acting force in the section is 100% P, as shown in the next slide.
Investigate the third route abcdeg.
For route abcdeg, the gross area is reduced by four hole areas, totalling 2.0 in^2, and three staggered distances exist. We will add the term S^2/4g*t to account for the additional area.
The s distance is 1.50 inches. We have three different g values: the first g is 2.50 inches, the second is 4.75 inches, and the last is 3 inches.
The sum of S^2/4g*t equals 0.265 inch2. The net area of that route equals 6.8-2.0+0.265=5.65 inch2
The route’s net area is not adjusted because the acting force in the section is 100% P, as shown in the next slide.
Investigate the fourth route acdeg
For route acdeg, the gross area is reduced by three hole areas, totalling 1.50 in^2, and two staggered distances exist. We will add the term S^2/4g*t to account for the additional area.
The s distance is 1.50 inches, and we have two different g values: g1 = 4.75 inches and g2 = 3.0 inches.
The sum of S^2/4g*t equals 0.153 inch2. The net area of that route equals 6.8-1.50+0.153=5.65 inch2
The route’s net area is to be adjusted. One bolt at the right side of the section transfers a P/10 load. The acting force in the section is 90% P, as shown in the next slide image. The adjusted net area will be 6.059 in^2.
Investigate the last route acdeg.
For the last route, acdeg, two hole areas are to be deducted. The net area equals 5.80inch2; there are no staggered lines. The net area is to be adjusted; two bolts are on the right side of the sections. The estimated area to be multiplied by 10/8 to account for 100% P of the load. The final net area equals 9.06 inch2.
What is the least net area for problem 3-7 for staggered bolts?
The minimum net area is 5.065 in^2 and belongs to the final route. abcdeg. The effective area for the lowest net area can be estimated by multiplying U by Anet.
The U value equals 1 since the angle is connected across all legs.
LRFD and ASD design strengths.
The LRFD design strength equals 220 kips; please refer to the next slide for more details about the estimation.
The lowest net area is 5.065 in^2 and belongs to the final route. abcdeg. The effective area for the lowest net area can be estimated by multiplying U by Anet.
The U value equals 1 since the angle is connected across all legs. The ASD design allowable strength equals 147 kips; please refer to the next slide for more details about the estimation.
The PDF file for this post can be viewed or downloaded from the following link.
This is a link to the previous post, solved 5-7 for block shear.
The following post is post15A-Solved problem 3-8-1 for staggered Bolts.
The next two posts are post 16 and Problem 3-4-3 for staggered bolt-tension members (1/2), and post 17-Problem 3-4-3 for MC section (LRFD and ASD values) (2/2).
There is a very useful external link, Block Shear Rupture–A Beginner’s Guide to the Steel Construction Manual, 14th ed.
There is a very useful external link, Block Shear Rupture–A Beginner’s Guide to the Steel Construction Manual, 15th ed.
There is a very useful external link, Block Shear Rupture–A Beginner’s Guide to the Steel Construction Manual, 16th ed.