PLASTIC DESIGN OF PORTAL FRAMES - Yavuz YARDIM · PLASTIC DESIGN OF PORTAL FRAMES Introduction This...
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PLASTIC DESIGN OF PORTAL FRAMES Introduction This section covers a number of features of plastic design of portal frames to BS 5950-1. The frame is analysed plastically allowing the formation of plastic hinges, which can rotate to allow the redistribution of bending moments. The frame is then designed in a similar way to a frame analysed elastically. However, there are some special clauses in BS 5950-1 for design based on plastic analysis, which will be covered in this section. Plastic analysis Simple plastic analysis, rather than elastic analysis, is commonly used for the design of portal frames as it results in relatively lightweight frames. The analysis is usually carried out by the use of specialist software, or by hand, using the basic principles of simple plastic theory. Plastic analysis assumes that plastic hinges occur at points in the frame where the value of the applied moment is equal to the plastic moment capacity of the member provided. Failure is deemed to have taken place when sufficient hinges have formed to create a mechanism. Having selected suitable member sizes, from strength considerations, the ultimate plastic collapse load of the frame is calculated. The ultimate load will generally be in the order of 5 to 10% greater than the design load due to the incremental range of member sizes. Plastic design methods result in relatively slender frames and checking frame stability is a basic requirement of the method. In addition, it is essential that local buckling and lateral distortion are also checked, because of the large strains at the hinge positions. In order to prevent local buckling it is essential that Class 1 plastic sections are selected, in accordance with Table 11 of BS 5950-1, at locations where hinges are required to rotate. Stability of the frame and individual members should be checked according to Section 5 of the code. Code requirements for plastic analysis • The loading should be predominately static i.e. fatigue is not a design criterion. • The steel should be grade S275, S355 or S460. • Special fabrication requirements are given for the tension flange within a distance D either side of the location of a plastic hinge. (D is the depth of the member). • Members with plastic hinges should be Class 1 plastic at the plastic hinge location. Cross-sections should also be symmetrical about the axis perpendicular to the axis of plastic hinge rotation. • At the plastic hinge location and either side of the plastic hinge until the moment in the member is less than 80% of the reduced moment capacity of the member, the net area of the cross-section (i.e. after deducting bolt holes) should be at least equal to the gross cross-section area divided by Ke. (Ke is 1.2 for S275 and 1.1 for S355). • For members with plastic hinges where the shear force is greater than 10% of the section shear capacity within a distance of D/2 of the plastic hinge, web stiffeners should be applied. Summary of design procedure Portal frame Monday, November 9, 2015 9:23 AM New Section 2 Page 1
Transcript of PLASTIC DESIGN OF PORTAL FRAMES - Yavuz YARDIM · PLASTIC DESIGN OF PORTAL FRAMES Introduction This...
PLASTIC DESIGN OF PORTAL FRAMES
IntroductionThis section covers a number of features of plastic design of portal frames to BS 5950-1. The frame is analysed plastically allowing the formation of plastic hinges, which can rotate to allow the redistribution of bending moments. The frame is then designed in a similar way to a frame analysed elastically. However, there are some special clauses in BS 5950-1 for design based on plastic analysis, which will be covered in this section.
Plastic analysisSimple plastic analysis, rather than elastic analysis, is commonly used for the design of portal frames as it results in relatively lightweight frames. The analysis is usually carried out by the use of specialist software, or by hand, using the basic principles of simple plastic theory.
Plastic analysis assumes that plastic hinges occur at points in the frame where the value of the applied moment is equal to the plastic moment capacity of the member provided. Failure is deemed to have taken place when sufficient hinges have formed to create a mechanism. Having selected suitable membersizes, from strength considerations, the ultimate plastic collapse load of the frame is calculated. The ultimate load will generally be in the order of 5 to 10% greater than the design load due to the incremental range of member sizes.
Plastic design methods result in relatively slender frames and checking frame stability is a basic requirement of the method. In addition, it is essential that local buckling and lateral distortion are also checked, because of the large strains at the hinge positions.
In order to prevent local buckling it is essential that Class 1 plastic sections are selected, in accordance with Table 11 of BS 5950-1, at locations where hinges are required to rotate. Stability of the frame and individual members should be checked according to Section 5 of the code.
Code requirements for plastic analysis
• The loading should be predominately static i.e. fatigue is not a design criterion.• The steel should be grade S275, S355 or S460.• Special fabrication requirements are given for the tension flange within a distance D either side of the location of a plastic hinge. (D is the depth of the member).• Members with plastic hinges should be Class 1 plastic at the plastic hinge location. Cross-sections should also be symmetrical about the axis perpendicular to the axis of plastic hinge rotation.• At the plastic hinge location and either side of the plastic hinge until the moment in the member is less than 80% of the reduced moment capacity of the member, the net area of the cross-section (i.e. after deducting bolt holes) should be at least equal to the gross cross-section area divided by Ke. (Ke
is 1.2 for S275 and 1.1 for S355).• For members with plastic hinges where the shear force is greater than 10% of the section shear capacity within a distance of D/2 of the plastic hinge, web stiffeners should be applied.
Summary of design procedure
Portal frameMonday, November 9, 2015 9:23 AM
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Assuming steel grade S275 for the rafter and column, the following trial sections are selected(N.B. these are first trials and may not be adequate):• Rafter 406 x 140 x39 kg UB Class1 Plastic Mcx = 199 kNm• Column 457 × 152 × 60 kg UB Class1 Plastic Mcx = 354 kNmBoth these sections are Class 1 plastic sections when classified using Table 11 of BS 5950-1.
Design checks
In-plane frame stabilityThe next stage is to check the overall stability of the frame. The main reason for this is thatthe only way to correct insufficient stability is to change the main member sizes. If any of theother checks are not satisfied than additional bracing can usually be added without altering
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other checks are not satisfied than additional bracing can usually be added without alteringmember sizes. Figure A.2 and Figure A.3 show the bending moment diagrams for the framefor vertical loading and horizontal loading, respectively.
As stated in Clause 5.5.4.1 of BS 5950-1, the in-plane stability may be checked using one ofthe following methods:(a) Sway check method (including the snap-through check)(b) Amplified moments methods(c) Second-order analysis.For plastic design the plastic load factor ( λp) must not be less than the required load factor ( λr).The sway check method will be used for this example. Therefore, the requirements ofBS 5950-1, Clause 5.5.4.2 need to be satisfied. Figure A.4 shows the haunch dimensionsrequired for the sway check equation.
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It is likely that Annex G of BS 5950-1 would allow the spacing of the restraints to be increased.Alternatively, the length between the lateral restraint adjacent to the plastic hinge (at S5) andthe next lateral restraint (at S3) could be checked (at say 3 m i.e. S2) by elastic methods (seeFigure A.8).
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Haunch stability - Annex G.2 approach
The calculation procedure for Annex G.2 is shown below. The requirements of Annex G.1.4for intermediate lateral restraints to the top flange also need to be satisfied.
Figure A.9 shows the haunch details and restraint locations. Annex G.2.2 of BS 5950-1 states that the following expression needs to be satisfied at points within the segment length. This example will consider points 1 to 5, see Figure A.9.
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