Table 1 Mechanical Properties of Pipe Table 2 Section Properties of Pipe and Reinforcing Dowel The Fitting with the Rib

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1 Table 1 Mechanical Properties o Pipe Material Minimum Minimum Allowable Modulus Tensile Yield Yield o trength trength trength* Elasticity (psi) (psi) (psi) (ksi) Aluminum 6063-T6 Pipe ATM429 30,000 25,000 18,000** 10,100 Aluminum 6061-T6 Pipe ATM429 38,000 35,000 24,000*** 10,100 Carbon teel tructural Tubing ATM A500 Grade B 58,000 42,000 25,500 Carbon teel Pipe ATM A53 Type F Grade B 48,000 30,000 21,600 Type E Grade B 60,000 35,000 25,000 Hollaender Tubular Dowel 6061-T6 38,000 35,000 24,000 10,100 *The allowable yield strength o aluminum pipe in bending is deined by the Aluminum Association to be (1.17 x Minimum Yield trength) / **Reduce to 8,000 within 1 inch o weld ***Reduce to 14,000 within 1 inch o weld Table 2 ection Properties o Pipe and Reinorcing Dowel Nominal Pipe ize OD ID Wall Area I (ips) (in.) (in.) Thickness (in. 2 ) (in. 4 ) (in. 3 ) chedule 10 1 ½ chedule 40 1 ¼ ½ chedule 80 1 ¼ ½ Hollaender Tubular Dowel Outside Diameter (OD), Inside Diameter (ID), Moment o Inertia (I), ection Modulus ()

2 Railing ystem Dimensions and Loads ymbols Used in Equations: w Uniorm loading, (lb/t). L pan between centerlines o posts or mounting brackets, (t). P Concentrated load applied to the top rail, (lb). h Height o post rom the top o the attachment to the point o load application, (in). h 1 Height o reinorcing insert inside post above the top o the attachment, (in). Bending stress, (psi). d Allowable yield strength or design, (psi). ection modulus, (in 3 ). 1 Combined section modulus o post with reinorcing insert, (in 3 ). Calculations or tructural Design The calculations used here are applicable to ree standing straight runs o guardrail with uniorm post spacing. The loads applied to a length o guardrail are deined by building codes as either a concentrated load applied to the top rail at any point in any direction, or as a uniormly distributed load per linear oot o rail applied to the top rail either horizontally and/or vertically downward. These two types o loads are not speciied to act concurrently. We will illustrate the design o a railing system using separate ormulas to calculate the stresses in the posts and the rails respectively. Typically the stress in the post will be the limiting actor on post spacing, pipe size/schedule, and material. Post Design Loads that are applied horizontally at the top rail o a guardrail system produce the maximum bending moment on the posts. The post acts as a vertical cantilevered member in resisting the horizontal load applied to the rails or posts. The height o the rail used in the calculations is measured rom the centerline o the top rail to the top o the attachment. A concentrated load applied to the rail at a post, is distributed to the posts on either side o that post. In railing systems where posts and rail are o identical material and section, and where post spacing varies between 3 eet and 6 eet, the greatest proportion o a concentrated load carried by any one post can be estimated as ollows: End posts: 2-span rail 85%; 3 or more spans 82%

3 Intermediate posts: 2-span rail 65%; 3 or more spans 60% In single span railing systems, each post shall be designed to carry the ull concentrated load. These are called the Load Proportion Factors, (P ). (A span is deined as the space between posts, 2-span3 posts, 3-span4 posts, etc.) A uniorm load is applied to the entire length o rail, and is speciied as pounds per linear oot o rail. The load carried by a given post is determined by the load per oot multiplied by the post spacing, or span, in eet. An end post will carry hal the load o an intermediate post. The ormulas or post design to calculate the bending stress in the post are as ollows: Concentrated Load: b P P h Uniorm Load: L h For calculations based on the allowable yield strength o the pipe, the calculated bending stress must be less than or equal to the allowable yield strength o the post material. Example 1: Concentrated loading condition using a Hollaender #52E-8 side mount lange, with an OHA concentrated load o 200 pounds, or a 3-span guardrail. Pipe: 1 ½ schedule 40; in 3 Rail height: h 43 in. (rom the centerline o the top rail to the top o the #52E-8 lange) Post spacing: 6 t. Based on the load distribution actors, the design load or an intermediate post is 60% o 200 lb, or 120 lb, and or an end post is 82% o 200 lb, or 164 lb. The bending stress in the intermediate post is: The bending stress in the end post is: , 828psi , 631psi.326 The 6063-T6 aluminum pipe, with an allowable design strength o 18,000 psi is acceptable or the intermediate post but not the end post. We can calculate the bending stress using a schedule 80 end post to see i this is acceptable: Pipe: 1 ½ schedule 80; in 3 The bending stress or the schedule 80 end post is: , 116 psi.412 This bending stress is less than the allowable design strength or 6063-T6 aluminum pipe. An easier way to do this would be to calculate or the required section modulus o the post i you had already chosen the type o pipe material you wanted to use by rearranging the ormula such as this: P P d h where, d the allowable design strength o the material. Example 2: Uniorm loading condition using a Hollaender #45BC-8 base lange with a 3 inch high barrel or the post mounting, and a uniorm loading condition o 50 pounds per oot applied horizontally. Pipe material: 6061-T6 aluminum alloy; d 24,000 psi Rail height: 38 in. (rom the centerline o the top rail to the top o the #45BC-8 lange) Post spacing: 6 t. There is no load distribution actor or the uniorm loading condition. Each intermediate post must take the load per linear oot multiplied by the post spacing in eet. The required section modulus is: in 24,000 This exceeds the section modulus or schedule 80 pipe that is in 3. We would either have to shorten the post spacing to 5.2 eet or reinorce the inside o the post with reinorcing dowel to increase the section 3

4 modulus at the top o the attachment. I this were side mounted rail with a 43 in. height, the post spacing would be reduced to 4.6 eet or a schedule 80 post. We would choose to use schedule 40 posts that would be reinorced internally with Hollaender Tubular Dowel made to it inside a schedule 40 post. The section modulus o schedule 40 pipe and the Hollaender π ( D d ) π ( ) Tubular Dowel would be: 0.547in 32D ( ) This is acceptable because it exceeds the required section modulus o in 3 or the #45BC-8 base lange, and the required section modulus o in 3 or a 43 inch rail height using the #52E-8 side mount lange. This will also reduce the cost o the rail since there will be ewer posts by holding the 6 oot post spacing vs. reducing the post spacing to meet the load. Also, the Hollaender Tubular Dowel is 60% lighter than the standard solid aluminum reinorcing dowel that is normally speciied, urther reducing the cost o the rail. An added beneit o the Hollaender Tubular Dowel over the solid dowel is that a weep hole is not required to let water drain rom the post. The required height o the Hollaender Tubular Dowel inside the schedule 40 post is given by: d 24, h1 h in L 50 6, say 12 inches. This is the height o the dowel above the top o the #45BC-8 base lange, which would make the total length o dowel or this lange to be 15 inches. For the #52E-8 side mount lange the dowel still has to reach the same height inside the post but it is longer because o the depth o the lange. The reinorcing dowel would be 22 inches long because the lange is 5 inches deep and the top o the lange is 2 inches below the walking surace. 3. Rail Design Ater we have designed the posts, we need to veriy that the rail will take the loads speciied by the applicable building code. These loads will be the same as speciied or the post design, i.e. concentrated or uniorm. A concentrated load applied to the top rail at any point, in any direction creates the maximum bending moment in the rail when applied at the mid-span o the rail between posts. The distribution o loads over multiple spans o rail decreases the maximum bending moment in rails. A bending moment constant (k) is used in the ormulas depending on the number o spans in the length o rail. The ormula to calculate the bending stress in the rail or concentrated loading at mid-span is as ollows: For single span rail k 4, or two or more spans k 5; P L k Example 3: Concentrated loading condition or a two span length o rail, with an OHA concentrated load o 200 pounds. Pipe: 1 ½ schedule 40, 6063-T6 aluminum; in 3, d 18,000 psi Post spacing: 72 in.. Bending moment constant: k 5 The bending stress in the rail is: , 834 psi The bending stress in the rail is less than the allowable yield strength o 6063-T6 aluminum pipe. I we increase the post spacing to the 8 oot maximum allowed by OHA, and this was a single span rail, the bending stress in the rail would be 14,723 psi which is still less than the allowable yield strength o 6063-T6 aluminum pipe.

5 However, even though OHA allows or a maximum 8 t. post spacing, all o the model building codes, BOCA, BC, and UBC or guardrail, speciy a uniorm load o 50 lb/t, and require that the loading conditions speciied must not exceed the allowable design working stress o the material. Thereore the post spacing will be limited to the most stringent requirement which is the values determined rom the post design calculations or a uniorm load. With a uniorm load, the rail load is proportional to the rail span, which has been established by the post design calculation. As in the concentrated load ormulas, a bending moment constant is used to allow or the distribution o loads over multiple spans. The ormula to calculate the bending stress in the rail or uniorm loading is as ollows: For one or two span rail k 96, or three or more spans k 114; L k Example 4: Uniorm loading condition o 50 pounds per oot horizontally and 100 pounds per oot vertically downward. This combined load resolves into pounds at 63 degrees rom horizontal. Pipe: 1 ½ schedule 40, 6061-T6 aluminum; in 3, d 24,000 psi Post spacing: 72 in. Bending moment constant: k 114 The bending stress in the rail is: , 594 psi The bending stress in the rail is less than the allowable yield strength o 6061-T6 aluminum pipe, so the 6 oot post spacing is acceptable with 1 ½ schedule 40 pipe or the rail. Reerences: Pipe Railing ystems Manual, Including Round Tube, third edition, Architectural Metal Products Division o The National Association o Architectural Metal Manuacturers, ANI/NAAM AMP , December 19, 1995 Metal Rail Manual, second edition, 1986, National Ornamental & Miscellaneous Metal Association 2