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62323: Architectural Structures II

Monther Dwaikat Assistant Professor Department of Building Engineering An-Najah National University. 62323: Architectural Structures II. Design of Beam-Columns. Beam-Column - Outline. Beam-Columns Moment Amplification Analysis Braced and Unbraced Frames

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62323: Architectural Structures II

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  1. Monther Dwaikat Assistant Professor Department of Building Engineering An-Najah National University 62323: Architectural Structures II Design ofBeam-Columns 68402

  2. Beam-Column - Outline • Beam-Columns • Moment Amplification Analysis • Braced and Unbraced Frames • Analysis/Design of Braced Frames • Design of Base Plates 68402

  3. Design for Flexure – LRFD Spec. • Commonly Used Sections: • I – shaped members (singly- and doubly-symmetric) • Square and Rectangular or round HSS 68402

  4. Beam-Columns • Likely failure modes due to combined bending and axial forces: • Bending and Tension: usually fail by yielding • Bending (uniaxial) and compression: Failure by buckling in the plane of bending, without torsion • Bending (strong axis) and compression: Failure by LTB • Bending (biaxial) and compression (torsionally stiff section): Failure by buckling in one of the principal directions. • Bending (biaxial) and compression (thin-walled section): failure by combined twisting and bending • Bending (biaxial) + torsion + compression: failure by combined twisting and bending 68402

  5. Beam-Columns • Structural elements subjected to combined flexural moments and axial loads are called beam-columns • The case of beam-columns usually appears in structural frames • The code requires that the sum of the load effects be smaller than the resistance of the elements • Thus: a column beam interaction can be written as • This means that a column subjected to axial load and moment will be able to carry less axial load than if no moment would exist. 68402

  6. Beam-Columns • AISC code makes a distinct difference between lightly and heavily axial loaded columns AISC Equation AISC Equation 68402

  7. Beam-Columns • Definitions Pu = factored axial compression load Pn = nominal compressive strength Mux = factored bending moment in the x-axis, including second-order effects Mnx = nominal moment strength in the x-axis Muy = same as Mux except for the y-axis Mny = same as Mnx except for the y-axis c = Strength reduction factor for compression members = 0.90 b = Strength reduction factor for flexural members = 0.90 68402

  8. Beam-Columns • The increase in slope for lightly axial-loaded columns represents the less effect of axial load compared to the heavily axial-loaded columns Unsafe Element Pu/fcPn Safe Element 0.2 Mu/fbMn These are design charts that are a bit conservative than behaviour envelopes 68402

  9. P P d M d x Moment Amplification • When a large axial load exists, the axial load produces moments due to any element deformation. • The final moment “M” is the sum of the original moment and the moment due to the axial load. The moment is therefore said to be amplified. • As the moment depends on the load and the original moment, the problem is nonlinear and thus it is called second-order problem. 68402

  10. Braced and Unbraced Frames • Two components of amplification moments can be observed in unbraced frames: • Moment due to member deflection (similar to braced frames) • Moment due to sidesway of the structure Unbraced Frames Member deflection Member sidesway 68402

  11. Unbraced and Braced Frames • In braced frames amplification moments can only happens due to member deflection Braced Frames Sidesway bracing system Member deflection 68402

  12. Unbraced and Braced Frames • Braced frames are those frames prevented from sidesway. • In this case the moment amplification equation can be simplified to: AISC Equation • KL/r for the axis of bending considered • K ≤ 1.0 68402

  13. Unbraced and Braced Frames • The coefficient Cm is used to represent the effect of end moments on the maximum deflection along the element (only for braced frames) • When there is transverse loading on the beam either of the following case applies 68402

  14. Ex. 5.1- Beam-Columns in Braced Frames A 3.6-m W12x96 is subjected to bending and compressive loads in a braced frame. It is bent in single curvature with equal and opposite end moments and is not loaded transversely. Use Grade 50 steel. Is the section satisfactory if Pu = 3200 kN and first-order moment Mntx = 240 kN.m Step I: From Section Property Table W12x96 (A = 18190 mm2, Ix = 347x106 mm4, Lp = 3.33 m, Lr = 14.25 m, Zx = 2409 mm3, Sx = 2147 mm3) 68402

  15. Ex. 5.1- Beam-Columns in Braced Frames Step II: Compute amplified moment - For a braced frame let K = 1.0 KxLx = KyLy = (1.0)(3.6) = 3.6 m - From Column Chapter: cPn = 4831 kN Pu/cPn = 3200/4831 = 0.662 > 0.2  Use eqn. - There is no lateral translation of the frame: Mlt = 0  Mux = B1Mntx Cm = 0.6 – 0.4(M1/M2) = 0.6 – 0.4(-240/240) = 1.0 Pe1 = 2EIx/(KxLx)2 = 2(200)(347x106)/(3600)2 = 52851 kN 68402

  16. Ex. 5.1- Beam-Columns in Braced Frames Mux= (1.073)(240) = 257.5 kN.m Step III: Compute moment capacity Since Lb = 3.6 m Lp< Lb< Lr 68402

  17. Ex. 5.1- Beam-Columns in Braced Frames Step IV: Check combined effect  Section is satisfactory 68402

  18. Ex. 5.2- Analysis of Beam-Column • Check the adequacy of an ASTM A992 W14x90 column subjected to an axial force of 2200 kN and a second order bending moment of 400 kN.m. The column is 4.2 m long, is bending about the strong axis. Assume: • ky = 1.0 • Lateral unbraced length of the compression flange is 4.2 m. 68402

  19. Ex. 5.2- Analysis of Beam-Column • Step I: Compute the capacities of the beam-column cPn = 4577 kN Mnx = 790 kN.m Mny = 380 kN.m • Step II: Check combined effect OK 68402

  20. Design of Beam-Columns • Trial-and-error procedure • Select trial section • Check appropriate interaction formula. • Repeat until section is satisfactory 68402

  21. Ex. 5.3 – Design-Beam Column • Select a W shape of A992 steel for the beam-column of the following figure. This member is part of a braced frame and is subjected to the service-load axial force and bending moments shown (the end shears are not shown). Bending is about the strong axis, and Kx = Ky = 1.0. Lateral support is provided only at the ends. Assume that B1 = 1.0. PD = 240 kN PL = 650 kN MD = 24.4 kN.m ML = 66.4 kN.m 4.8 m MD = 24.4 kN.m ML = 66.4 kN.m 68402

  22. Ex. 5.3 – Design-Beam Column • Step I: Compute the factored axial load and bending moments Pu = 1.2PD + 1.6PL = 1.2(240)+ 1.6(650) = 1328 kN. Mntx = 1.2MD + 1.6ML = 1.2(24.4)+ 1.6(66.4) = 135.5 kN.m. B1 = 1.0  Mux = B1Mntx = 1.0(135.5) = 135.5 kN.m • Step II: compute Mnx, Pn • The effective length for compression and the unbraced length for bending are the same = KL = Lb = 4.8 m. • The bending is uniform over the unbraced length , so Cb=1.0 • Try a W10X60 with Pn = 2369 kN and Mnx= 344 kN.m 68402

  23. Ex. 5.3 – Design-Beam Column • Step III: Check interaction equation • Step IV: Make sure that this is the lightest possible section.  Try W12x58 with Pn = 2247 kN and Mnx= 386 kN.m  Use a W12 x 58 section OK 68402

  24. Design of Base Plates • We are looking for design of concentrically loaded columns. These base plates are connected using anchor bolts to concrete or masonry footings • The column load shall spread over a large area of the bearing surface underneath the base plate AISC Manual Part 16, J8 68402

  25. Design of Base Plates • The design approach presented here combines three design approaches for light, heavy loaded, small and large concentrically loaded base plates Area of Plate is computed such that n m B 0.8 bf where: If plate covers the area of the footing 0.95d N If plate covers part of the area of the footing • The dimensions of the plate are computed such that m and n are approximately equal. A1 = area of base plate A2 = area of footing f’c = compressive strength of concrete used for footing 68402

  26. Nominal bearing strength Design of Base Plates Thickness of plate However  may be conservatively taken as 1 68402

  27. Ex. 5.4 – Design of Base Plate • For the column base shown in the figure, design a base plate if the factored load on the column is 10000 kN. Assume 3 m x 3 m concrete footing with concrete strength of 20 MPa. N 0.95d W14x211 0.8bf B 68402

  28. Ex. 5.4 - Design of Base Plate • Step I: Plate dimensions • Assume thus: • Assume m = n • N = 729.8 mm say N = 730 mm B = 671.8 mm say B = 680 mm 68402

  29. Ex. 5.4 - Design of Base Plate • Step II: Plate thickness 68402

  30. Ex. 5.4 - Design of Base Plate • Selecting the largest cantilever length • use 730 mm x 670 mm x 80 mm Plate 68402

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