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324

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Civil Engineering

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Oct 30, 2023

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1 CIE 324 – Introduction to Structural Design Assignment #1 – Design concepts Introduction : In subsequent assignments, we will systematically take on design of structures such as buildings and bridges that are most commonly encountered in civil engineering practice. Before doing so, in this assignment, we design a very simple structure – a support frame for a swing set. In practice, such a structure will likely never be designed using the formal process we will adopt here; instead, standardized designs based on experience will likely be deployed. Nevertheless, since this is a structure we are all familiar with, we use it as a vehicle to accomplish the following: 1. Appreciate how user requirements define design choices. 2. Become comfortable with the idea that the design process is open-ended; unlike your most common experience in classes thus far, there is no unique right answer. 3. Understand how variabilities/uncertainties must be accounted for in determining structural loads. 4. Learn about strength and serviceability limit states. 5. Apply concepts of load cases, load factors and load combinations to compute worst-case load effects (internal forces) in structural members. 6. Understand the role played by structure analysis in design. 7. Tie some basic notions of member strengths (capacities) with concepts you learned in mechanics of solids. 8. Understand how variabilities in member strength must be accounted for. 9. See how the design process is iterative. 10. Recognize that design is a fun and creative exercise, and not rote application of formulas. The structure : A conceptual layout of a support structure for a swing set consisting of two swings is shown in the figure below along with elevation and plan views with the different dimensions marked. The structure consists of three types of members – those making up the two A-frames, the horizontal beam from which the swings are hung, and the braces. The members are to be pipes made of ASTM A53 Grade B Steel ( 𝐸𝐸 = 29,000 𝑘𝑘𝑘𝑘𝑘𝑘 , 𝜎𝜎 𝑦𝑦 = 35 𝑘𝑘𝑘𝑘𝑘𝑘 ), and welded together. The A-frame members and the braces are bolted to threaded rods embedded in concrete blocks buried in the ground. A-frame Beam Brace Swing 1 Swing 2 h l a b Elevation Plan w w s s

2 Design tasks: (NOTE: While the following is the general way the logic develops, your work may not progress exactly in this sequence; you may find yourself going back and forth between tasks) 1. Choose suitable values for the dimensions h , l , w , w s , s , a, and b . Justify your choices very briefly. === Design Loads=== 2. Estimate loads on the structure. a. Assume that the predominant loads are from the swings, and that other loads such as due to wind are comparatively small (this will not be the case for structures we look at in subsequent assignments) [No answer required]. b. What factors determine the loads? Perhaps you have to consider if the swings are exclusively to be used by children, or if adults are likely to use it? c. What load does a swing apply on the beam when the swing is in the vertical position? Weight, centrifugal force, anything else? d. What load needs to be considered when a swing is in an inclined configuration? Determine the inclined angle that provides the maximum tension on the rope. e. What are potential sources of variability in the load estimates in the vertical and inclined configurations? 3. Load cases – create the following 6 load cases [No answer required] a. Load case 1: swing 1 vertical b. Load case 2: swing 1 inclined c. Load case 3: swing 2 vertical d. Load case 4: swing 2 inclined e. Load case 5: swing 1 not in vertical plane f. Load case 6: swing 2 not in vertical plane 4. Load combinations - Based on what you think is the extent of variability associated with each load case, assign load factors, and create load combinations. Explain your reasoning for your selection of these load factors. === Preliminary Component Design=== 5. Preliminary section properties to start structural analysis a. We are now confronted with how to assign section properties – to decide on what size pipe section to use for each member, we must know what the maximum internal force in the member is; to know this, we must perform a structural analysis; however, to perform a structural analysis, we need section properties! [No answer required] b. To break this cycle, we must come up with some reasonable section properties to bootstrap the analysis. We can then revise these sections based on internal forces arising from loads (demand) and member strength (capacity) [No answer required]. c. Devise an approach to come up with preliminary sections to start the analysis. Check the proper details in Problems 9-10. i. For the beam, consider the 4-point bending conditions, where two middle-point loads come from the swings. Check both the serviceability and the strength limit. For the serviceability, determine the required second moment of area, 𝐼𝐼 , by considering an allowable displacement. For the strength limit, determine the required section modulus, Z, to prevent the yield of steel.

3 ii. For the braces, approximate them as columns. Determine the required second moment of area, 𝐼𝐼 , to prevent their column buckling. === Structural Analysis === 6. Model the geometry of the structure in LARSA a. Create a customized material model for ASTM A53 Grade B steel if you do not see it in LARSA. b. Model the geometry – joint coordinates and member connectivity c. Determine the boundary conditions of the supports. 7. Perform a structural analysis and determine from the different load combinations, the worst-case internal force (axial force or bending moment) for each member, and worst-case reaction (for future foundation design). Summarize the following in the form of a table. a. Maximum bending moment in the beam b. Maximum compressive force in the A-frame members c. Maximum compressive force in the braces d. Maximum upward and downward (resisting uplift) reactions 8. Verify results obtained from LARSA using simple hand calculations based on equilibrium; such supporting calculations must always be performed when interpreting results from computer programs to make sure that the analysis was set up correctly in the program. Specifically, compare a. Maximum bending moment in the beam obtained from one load combination b. Uplift reaction from one load combination involving inclined loads === Component Design=== 9. Strength limit state a. For long pipes arranged in this fashion, nominal capacities may be simplistically established as follows: i. Tension: 𝑁𝑁 = 𝜎𝜎 𝑦𝑦 𝐴𝐴 = 𝐹𝐹 𝑦𝑦 𝐴𝐴 ii. Compression: 𝑃𝑃 = 𝐸𝐸𝐼𝐼 � 𝜋𝜋 𝐿𝐿 � 2 iii. Bending: 𝑀𝑀 = 𝜎𝜎 𝑦𝑦 𝑍𝑍 = 𝐹𝐹 𝑦𝑦 𝑍𝑍 b. Based on your knowledge from mechanics of solids, explain in once sentence each, the origin of each of these formulas. [Note that this way of computing capacities is highly simplistic and is used for the purposes of this assignment; we will learn much more about member capacity computation in future assignments] c. Using a resistance factor of 0.9, check all the members for capacity, and summarize your findings in a table. 10. Serviceability limit state – Determine the maximum deflection at midspan of the beam under unfactored load combinations, and check whether this is acceptable. Typically, the acceptable deflection is stated as a fraction of the span, for example 𝑤𝑤 /300 . In this case, this would be determined based on comfort, a lot of deflection while swinging would be uncomfortable. === Epilogue=== 11. We conclude this assignment at this stage, but the next step would be to revise member sizes and repeat the analysis until the strength and serviceability checks are satisfied [No answer required]. 12. Briefly reflect upon how you feel the 10 objectives listed at the beginning of the assignment were met.

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