Steel Post Load Analysis

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Jasmine Golden
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1 Steel Post Load Analysis Scope The steel posts in , , and , are considered to be traditional building products. According to the 2015 International Building Code, this type of product need only be proven to comply with regulations by way of written calculations. The following document will describe the post s performance requirements outlined in the IBC and IRC and show the appropriate calculations needed for compliance. This analysis is also valid for the 2009 & 2012 IBC/ IRC. Key Terms and Definitions Elastic Section Modulus (S): A geometric property for a given cross-section used in the design of beams or flexural members. The elastic section modulus is defined as S=I / y, where I is the second moment of inertia and y is the distance from the neutral axis to any given fiber. Modulus of Elasticity (E): The elastic modulus of an object is defined as the slope of its stressstrain curve in the elastic deformation region. Yield Strength (σ): The stress at which a predetermined amount of permanent deformation occurs. Second Moment of Inertia (I): A property of a cross-section that can be used to predict the resistance of a beam to bending and deflection around an axis that lies in the cross-sectional plane. Factor of Safety (FOS): Term describing the structural capacity of a system beyond the expected loads or actual loads. Load Distribution: Before analysis can be completed on the structural posts of a metal railing system, it must be determined if a Load Proportion Factor can be applied. In certain circumstances, a post is allowed a percent reduction in total load resistance requirements, assuming that adjacent posts and rails will take a percentage of any applied load. This reduction is called the Load Proportion Factor (Pf). The percentage is determined by the ratio of the stiffness of the rail (Kr) relative to the stiffness of the post (Kp). Calculation of the Stiffness Ratio (Rr) and the corresponding Load Proportion Factor are explained below. In preparing for the worst case scenario, there will be no application of a load proportion factor in these calculations. 1 of 11

2 Structural Post Load Analysis According to metal railing requirements, the bending moment (BM) on a post is defined as the horizontal load multiplied by the height of the load. This value cannot be greater than the resisting moment (RM), which is defined as the allowable design stress multiplied by the section modulus. Equations for post analysis: Bending Moment: BM = P h Resisting Moment: RM = σy S / Ωb Using the section modulus of the steel post, it can be shown that the posts more than exceed the requirements of the governing equations. Calculations of Post Section Modulus: The steel structural posts, and are made of steel grade q235 welded to a 3.7 mounting flange. The steel structural post, , is made from the same material but is not welded to a mounting flange. The cross section and section modulus for these structural posts can be seen below. For consistency, the geometrical properties of the post have been attained through the use of SolidWorks Section properties of the steel structural post in Area = inches^2 Centroid relative to output coordinate system origin: ( inches ) X = Y = Z = Moments of inertia of the area, at the centroid: ( inches ^ 4 ) Lxx = Lxy = Lxz = Lyx = Lyy = Lyz = Lzx = Lzy = Lzz = Polar moment of inertia of the area, at the centroid = inches ^ 4 Angle between principal axes and part axes = degrees Principal moments of inertia of the area, at the centroid: ( inches ^ 4 ) Ix = Iy = of 11

3 With the Moment of Inertia from SolidWorks, the section modulus of the steel post can be found. Section Modulus for : Section properties of the steel structural post in Area = inches^2 Centroid relative to output coordinate system origin: ( inches ) X = Y = Z = Moments of inertia of the area, at the centroid: ( inches ^ 4 ) Lxx = Lxy = Lxz = Lyx = Lyy = Lyz = Lzx = Lzy = Lzz = Polar moment of inertia of the area, at the centroid = inches ^ 4 Angle between principal axes and part axes = degrees Principal moments of inertia of the area, at the centroid: ( inches ^ 4 ) Ix = Iy = Section Modulus for : 3 of 11

4 Section properties of the steel structural post in Area = inches^2 Centroid relative to output coordinate system origin: ( inches ) X = Y = Z = Moments of inertia of the area, at the centroid: ( inches ^ 4 ) Lxx = Lxy = Lxz = Lyx = Lyy = Lyz = Lzx = Lzy = Lzz = Polar moment of inertia of the area, at the centroid = inches ^ 4 Angle between principal axes and part axes = degrees Principal moments of inertia of the area, at the centroid: ( inches ^ 4 ) Ix = Iy = Section Modulus for : Determination of appropriate Bending Moment: This analysis will be calculated showing the worst case scenario, which occurs when the force is applied at the top of the steel structural These calculations will show the resisting moment for each of the steel structural posts, , , and The factor of safety for each post will be calculated by taking the ratio of the resisting moment to the bending moment of each post. 4 of 11

5 The following post analysis will be based on the material properties of steel grade q235. The yield strength of grade q235 steel is 235 MPa or 34,084 psi. Ωb = 1.67 (AISC F1) According to the 2015 IBC, a structural steel post must undergo a 200 lb point load (P) at any point on top of the post. Maximum post spacing with railing attached to only one side is 8ft. 50plf uniform load along rail will result in 200 lb point load. This case shall be examined as it represents the largest possible bending moment. 5 of 11

6 Calculations for Resulting Factor of Safety: Calculations for Resulting Factor of Safety: Calculations for Resulting Factor of Safety: With the above calculations, it is proven that the resisting moment in each post is larger than the bending moment caused by the load, showing that the post exceeds design requirements. 6 of 11

7 Post Fastener Considerations Through Bolt Application for Commercial Posts The force at the bottom of the post/plate must be calculated and then compared to the resisting moment and shear exerted by the fasteners. The same calculation method will be used for the analysis for all four steel structural posts. The structure supporting the post and the connection from the post to the structure must be designed to resist the listed shear load and the listed tension/compression load. The design of the supporting structure and the connection to the structure are the responsibility of others. Sample connection show below for illustration purposes only. 7 of 11

8 Fastener Calculations for Given a 200lb point load at the very top of the post, the bending moment can be determined. This bending moment results in a tension/compression force at the bottom of the base plate. This force is a function of the bending moment (BM) and the distance ( ) between the fasteners. Forces at the bottom of the post: Fastener Calculations for tlb This bending moment results in a tension/compression force at the bottom of the base plate. This force is a function of the bending moment (BM) and the distance ( ) between the fasteners. Forces at the bottom of the post: Fastener Calculations for This bending moment results in a tension/compression force at the bottom of the base plate. This force is a function of the bending moment (BM) and the distance ( ) between the fasteners. Forces at the bottom of the post: b 8 of 11

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5. What is the moment of inertia about the x - x axis of the rectangular beam shown?

5. What is the moment of inertia about the x - x axis of the rectangular beam shown? 1 of 5 Continuing Education Course #274 What Every Engineer Should Know About Structures Part D - Bending Strength Of Materials NOTE: The following question was revised on 15 August 2018 1. The moment