Assignment 1 - Structutral Design I: Analysis and Design of Simply Supported Beams

1 University of Southern Queensland Faculty of Health Engineering and Sciences Assignment 1 CIV2503 STRUCTURAL DESIGN I Due 22 August 2022 Marks 200 Note to students This assignment uses the last three digits denoted x y z of your student ID number to individualise your design data Student must use these three digits to obtain your own design data For example a student with ID number of 0060123456 will have x 4 y 5 z 6 Use 4 significant figures for midstep values and 3 significant figures for the value of a final answer Question 1 60 marks A simply supported beam has a span of 8 m and is subject to a half distributed load w 3x 0z kNm and a concentrated load P 10y 0z kN as shown in Figure 1 The beam is made of OneSteel 300PLUS universal beam section 410UB 537 with E200x103 MPa and loaded in its strong axis direction For simplicity you can ignore the beam selfweight Use the method of superposition and carry out the following tasks a Analyse and draw neat labelled Shear Force and Bending Moment Diagrams for the beam ie for each of the given individual loads and then superpose for the combined loading Find critical values of Shear Force and Bending Moment for strength design 30 marks b Determine the total maximum deflection of the beam using approximate method not the exactrigorous methods from CIV3505 Then evaluate it against the deflection limit span250 and give comments 20 marks c State all possible solutions on how to reduce the deflection of beam assuming you are not subject to any design constraints 10 marks Figure 1 Simply Supported Beam Example A student with xyz 456 will have w 34 06 4 kNm P 105 06 111 kN Question 2 70 marks a An indeterminate beam is subject to a two distributed loads w1 6x 0z kNm and w2 5y 0z kNm as shown in Figure 2 Analyse and indicate where you would add conceptual pins to convert this to a corresponding determinate beam 15 marks b Using the approximate method with conceptual pins analyse and draw a neat and fully labelled Bending Moment Diagram showing all critical values and other necessary details for the beam Include all the working for part marks 45 marks 2 m 2 m 4 m 8 m 2 c Summarise the differences in design load effects ie shears moments and deflections between using a continuous beam of 4 equal spans and using 4 identical simply supported beams to cover the same length Some extra beam formulae are included in the final page to complement those already provided in the learning materials 10 marks Figure 2 Indeterminate Beam Example A student with xyz 456 will have w1 64 06 7 kNm w2 55 06 61 kNm Question 3 70 marks Plan view of a steel portal frame building with a 3 m cantilever roof on one side is shown in Figure 3 Roof layers roof sheeting insulation and roof bracing are supported by purlins which are in turn supported by universal beams B1 to B5 There is a mechanical equipment hung at bottom of beam B3 causing a dead load PG 6x kN and a live load PQ 4y kN both unfactored a Develop line load diagrams using the basic design load combination 12G 15Q for the following members i A typical purlin 15 marks ii Beam B1 20 marks iii Beam B3 25 marks b Calculate the basic design load combination 12G 15Q axial applied at the top of column Y3 10 marks Roof sheeting selfweight allowance g1 005z kPa selfweight of insulation and roof bracing g2 6z kgm2 For selfweights of beams 360UB567 and purlins Z15015 see OneSteel and Lysaght catalogues Use Table 32 of ASNZS 11701 to determine imposed action on roof using only distributed load is sufficient 3 10000 3000 X Y Z Figure 3 Plan view of portal frame building Example A student with xyz 456 will have PG 64 kN PQ 45 kN g1 0056 kPa g2 66 kgm2 Final note to students See overpage for some extra beam formulae for question 2 3000 1 5000 2 5000 purlin at 1250 mm centres mechanical equipment hanged at this point 3 5000 4 5000 5 B1 B3 B5 B4 B2 FBD SFD BMD R₁ V₄ R₄ V₄ 0400wL R₂ R₃ 110wL V₂₁ V₃ 0500wL V₂₂ V₃ 0600wL M₁ M₅ at 0400L from R₁ or R₄ 0080wL² M₂ M₄ at R₂ or R₃ 0100wL² M₃ at mid centre span 0025wL² Maximum deflection ₘₐₓ at 0446L from R₁ or R₄ 00069wL⁴ EI FBD SFD BMD R₁ V₁ R₅ V₅ 0393wL R₂ R₄ 1143wL R₃ 0928wL V₂₁ V₂₄ 0607wL V₂₂ V₄ 0536wL V₃ 046wL M₁ at 0393L from R₁ M₄ at 0393L from R₅ 00772wL² M₂ at R₂ 01071wL² M₃ at 0536L from R₂ M₅ at 0536L from R₄ 00364wL² M₄ at R₃ 0071wL² Maximum deflection ₘₐₓ at 0440L from R₁ and R₃ 00065wL⁴ EI