CIVL5266 - Steel Structures - Stability: Semester 1, 2024
Assignment 3: Direct Design Method (DDM) Project (25%)
Important Notes:
. Due date: Before Monday 11:59pm (03 June 2024)
. Requirements: You are requested to upload a single pdf file.
. How to submit: All assignments are submitted online on the Assignments page on Canvas.
. Late submissions: Late submissions will be accepted, however 5% of the total mark will be subtracted per day late.
Question 1: Continuous Beam Design by Elastic and Inelastic Analyses
Consider the continuous three-member beam shown in Fig. 1. All three members are oriented for major-axis bending, and fully braced out-of-plane. Neglect the self-weight of the members. The steel has a yield stress of 320 MPa, a Young’s modulus of 200 GPa, G = 80000MPa. The steel is elastic-perfectly-plastic.
Figure 1.
Perform the case studies defined below for the following two design methods:
a. First-order elastic analysis in AS4100. Use the resistance factor for flexural members as specified in AS4100.
b. Second-order inelastic analysis (Direct Design Method). Use a system resistance factor of 0.9.
Case studies:
1) Given that all members are 410UB53.7, determine the largest value for Pu that is permitted by each of the above design methods.
2) Given that member AB is a 610UB125, member BC is a 410UB53.7, and member CD is a 410UB59.7, determine the largest value for Pu that is permitted by each of the above design methods.
Table 1.
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Member Lengths and Sizes
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Design Method
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AB
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BC
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CD
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Pu
kN
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Case 1
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AS4100-Elastic
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410UB53.7
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410UB53.7
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410UB53.7
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DDM
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410UB53.7
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410UB53.7
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410UB53.7
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Case 2
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AS4100-Elastic
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610UB125
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410UB53.7
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410UB59.7
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DDM
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610UB125
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410UB53.7
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410UB59.7
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Table 2.
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Plastic Hinge Sequence
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1st Hinge
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2nd Hinge
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3rd Hinge
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Case
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Applied load
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Location
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Applied load
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Location
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Applied load
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Location
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1
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2
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Last digit of SID
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a (m)
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b (m)
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1; 4; 7
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2.5
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3.0
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2; 5; 8
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3.0
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2.5
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0; 3; 6; 9
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3.5
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2.0
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Hints:
1) Given that the members are fully laterally braced, 2-dimensional analyses are sufficient.
2) Results of first-order elastic analyses are directly proportional to the applied load; for example, doubling the applied load will result in doubling the internal forces and moments.
3) Given that the strength limit state in this study will always be controlled by the formation of a plastic mechanism, the computational models do not need to account for the effects of initial geometric imperfections.
4) If the yield ratio of a cross-section exceeds 70%, it is assumed that a plastic hinge has developed.
5) Use eight elements for each beam sector.
Questions
1) Complete Table 1. Give calculation details, show how the largest value of Pu for the AS4100 elastic method is determined. Which member is the critical member?
2) For the two cases of DDM, plot the load versus displacement response, in which the displacement = vertical displacement at the point load.
3) For the two cases of DDM, complete Table 2 to record the data related to the plastic hinge sequence.
4) What level of additional load capacity was realized by employing the DDM in Cases 1 and 2 than the AS4100 elastic design method? In your opinion, is this significant and worth the additional effort a completing an inelastic analysis?
5) Engineers have often stated that the design of compact fully laterally braced beams by elastic analysis can be defined as a process of designing for the first plastic hinge. Based on the results of this study, do you agree or disagree? Justify your response.
6) For this system and given applied loading, is it possible for a plastic hinge to ever form at support points A and D? Justify your response.
7) If the beam is supported in the same manner but is not continuous at points B and C, what would the maximum concentrated load Pu be for cases 1 and 2, given by the AS4100 elastic method and the DDM? What can you conclude about the benefits of using the DDM to design a statically indeterminate system?
Question 2: Planar frame design by Elastic and Inelastic Analyses
Consider the planar frame shown in Fig. 2. All members are oriented for major-axis bending, and fully braced out-of-plane. Neglect the self-weight of the members. Assume that the structural system is a braced frame.
The steel has a yield strength of 320 MPa, a Young’s modulus of 200 GPa, and shear modulus G = 80000MPa. The steel is elastic-perfectly-plastic.
Figure 2. Two-bay two-story planar frame.
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C1=310UB32
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C2=610UB101
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C3=C5=C6=530UB92.4
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C4=150UB14
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B1=700WB173
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B2=900WB218
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B3=530UB92.4
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B4=700WB173
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UB=universal beam; WB=welded beam
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Last digit of SID
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c (m)
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d (m)
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1; 4; 7
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6.0
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10.0
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2; 5; 8
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5.0
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11.0
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0; 3; 6; 9
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4.0
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12.0
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Perform the case studies defined below for the following design methods:
a. Conventional method in AS4100
b. Direct Design Method (second-order inelastic analysis).
Determine the largest value for r that is permitted by each of the above design methods. For simplicity, start with r = 50 kN/m.
1) Given that the members are fully laterally braced, 2-dimensional analyses are sufficient.
2) For the elastic method in AS4100, use the resistance factor as specified in AS4100.
3) For the DDM, use a system resistance factor of 0.9.
4) For the DDM, include a frame initial out-of-plumbness of H/500, in which H is the height of the frame. Neglect member initial out-of-straightness.
5) If the yield ratio of a cross-section exceeds 70%, it is assumed that a plastic hinge has developed.
6) Use eight elements for each member.
Questions
1) When modelling the initial frame out-of-plumbness, the columns can lean to the left, or to the right. Which direction will you use? Justify your answer.
2) Give calculation details, show how the largest value of P for the AS4100 method (second- order elastic analysis) is determined. Which member is the critical member?
3) For the DDM, plot the load versus displacement response, in which the displacement = horizontal roof displacement at the left roof corner.
4) At the largest value of P determined by DDM, show the locations of the plastic hinge(s) that have developed. Explain the plastic hinge sequence. What is the failure mode of the frame?
5) What level of additional load capacity was realized by employing the DDM as compared to the AS4100 elastic method? In your opinion, is this significant and worth the additional effort a completing an inelastic analysis?
6) Engineers have often stated that the design of compact fully laterally braced frames by elastic analysis can be defined as a process of designing for the first plastic hinge. Based on the results of this study, do you agree or disagree? Justify your response.