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19 Pages

### lect21

Course: ENDS 231, Fall 2008
School: Texas A&M
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Word Count: 555

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STRUCTURES ARCHITECTURAL I: STATICS AND STRENGTH OF MATERIALS ENDS 231 DR. ANNE NICHOLS SPRING 2008 twenty one beams: deflection &amp; design Beam Deflection &amp; Design 1 Lecture 21 Architectural Structures I ENDS 231 S2008abn lecture Design for Strength +... strength design forces &amp; material serviceability limit deflection and cracking control noise &amp; vibration no excessive...

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STRUCTURES ARCHITECTURAL I: STATICS AND STRENGTH OF MATERIALS ENDS 231 DR. ANNE NICHOLS SPRING 2008 twenty one beams: deflection & design Beam Deflection & Design 1 Lecture 21 Architectural Structures I ENDS 231 S2008abn lecture Design for Strength +... strength design forces & material serviceability limit deflection and cracking control noise & vibration no excessive settlement of foundations durability appearance component damage ponding Beam Deflection & Design 2 Lecture 21 Architectural Structures I ENDS 231 S2008abn Beam Deformations curvature relates to bending moment modulus of elasticity moment of inertia 1 M = R EI c R L y Beam Deflection & Design 3 Lecture 21 Architectural Structures I ENDS 231 M ( x) curvature = EI M ( x) = slope = dx EI M ( x) = deflection = dx EI S2008abn Deflected Shape & M(x) -M(x) gives shape indication boundary conditions must be met Beam Deflection & Design 4 Lecture 21 Architectural Structures I ENDS 231 S2008abn Boundary Conditions at pins, rollers, fixed supports: y = 0 at fixed supports: = 0 at inflection points from symmetry: = 0 ymax at Beam Deflection & Design 5 Lecture 21 dy =0 dx Architectural Structures I ENDS 231 S2008abn Superpositioning if w can be superpositioned & y can elastic range only! + = Beam Deflection & Design 6 Lecture 21 Architectural Structures I ENDS 231 S2008abn Deflection Limits based on service condition, severity Use LL only Roof beams: Industrial L/180 Commercial plaster ceiling L/240 no plaster L/360 Floor beams: Ordinary Usage L/360 Roof or floor (damageable elements) Beam Deflection & Design 7 Lecture 21 Architectural Structures I ENDS 231 DL+LL L/120 L/180 L/240 L/240 L/480 S2008abn Lateral Buckling lateral buckling caused by compressive forces at top coupled with insufficient rigidity can occur at low stress levels stiffen, brace or bigger Iy Beam Deflection & Design 8 Lecture 21 Architectural Structures I ENDS 231 S2008abn Local Buckling steel I beams flange in buckle direction of smaller radius of gyration web force crippling Beam Deflection & Design 9 Lecture 21 Architectural Structures I ENDS 231 S2008abn Local Buckling web flange Beam Deflection & Design 10 Lecture 21 Architectural Structures I ENDS 231 S2008abn Shear in Web panels in plate girders or webs with large shear buckling in compression direction add stiffeners Beam Deflection & Design 11 Lecture 21 Architectural Structures I ENDS 231 S2008abn Shear in Web plate girders and stiffeners Beam Deflection & Design 12 Lecture 21 Architectural Structures I ENDS 231 S2008abn Beam Design 1. Know Fall for the material or FU for LRFD 2. Draw V & M, finding Mmax 3. Calculate Sreqd h ( f b Fb ) b 4. Determine section size Beam Deflection & Design 13 Lecture 21 Architectural Structures I ENDS 231 bh S= 6 2 S2008abn Beam Design 4*. Include self weight for Mmax and repeat 3 & 4 if necessary 5. Consider lateral stability Unbraced roof trusses were blown down in 1999 at this project in Moscow, Idaho. Photo: Ken Carper Beam Deflection & Design 14 Lecture 21 Architectural Structures I ENDS 231 S2008abn Beam Design 6. Evaluate shear stresses - horizontal ( f v F...

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