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A RCHITECTURAL S TRUCTURES : Equilibrium Method F ORM, B EHAVIOR, AND D ESIGN ARCH 331 important places D R. A NNE N ICHOLS supports S PRING 2019 concentrated loads lecture eight start and end of distributed loads

  1. A RCHITECTURAL S TRUCTURES : Equilibrium Method F ORM, B EHAVIOR, AND D ESIGN ARCH 331 • important places D R. A NNE N ICHOLS – supports S PRING 2019 – concentrated loads lecture eight – start and end of distributed loads – concentrated moments • free ends – zero forces shear & bending moment diagrams Forum, Pompeii V & M Diagrams 1 Architectural Structures F2009abn V & M Diagrams 2 Foundations Structures F2008abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 Semigraphical Method Semigraphical Method • by knowing • relationships – area under loading curve = change in V – area under shear curve = change in M – concentrated forces cause “ jump ” in V – concentrated moments cause “ jump ” in M x x D D        M M Vdx V V wdx D C D C x x C C V & M Diagrams 4 Foundations Structures F2008abn V & M Diagrams 3 Foundations Structures F2008abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 1

  2. Semigraphical Method Curve Relationships • integration of functions • M max occurs where V = 0 (calculus) • line with 0 slope, integrates to sloped y y no area V L +  - x x M + L • ex: load to shear, shear to moment V & M Diagrams 5 Foundations Structures F2008abn V & M Diagrams 6 Foundations Structures F2008abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 Curve Relationships Curve Relationships • parabola, integrates to 3 rd order curve • line with slope, integrates to parabola y y y y   x x x x • ex: load to shear, shear to moment • ex: load to shear, shear to moment V & M Diagrams 7 Foundations Structures F2008abn V & M Diagrams 8 Foundations Structures F2008abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 2

  3. Basic Procedure Basic Procedure 1. Find reaction forces & moments M: Plot axes, underneath beam load 6. Starting at left diagram 7. Moment is 0 at free ends V: 8. Moment jumps with moment 2. Starting at left 9. Moment changes with area under V 3. Shear is 0 at free ends 10.Maximum moment is where shear = 0! 4. Shear jumps with concentrated load (locate where V = 0) 5. Shear changes with area under load V & M Diagrams 9 Foundations Structures F2008abn V & M Diagrams 10 Foundations Structures F2008abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 Parabolic Shapes Shear Through Zero • cases • slope of V is w (-w:1) w (force/length) - - - + + load V     x w V x A height = V A A w shear up fast, down slow, up slow, down fast, A width = x then slow then fast then fast then slow V & M Diagrams 12 Foundations Structures F2008abn Lecture 8 ARCH 331 V & M Diagrams 11 Foundations Structures F2008abn Lecture 8 ARCH 331 3

  4. Deflected Shape & M(x) Boundary Conditions • at pins, rollers, • -M(x) gives shape indication fixed supports: y = 0 • boundary conditions must be met • at fixed supports:  = 0 • at inflection points from symmetry:  = 0 dy • y max at  0 dx V & M Diagrams 14 Foundations Structures F2008abn V & M Diagrams 13 Foundations Structures F2008abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 Tabulated Beam Formulas Tools • • software & spreadsheets help how to read charts • http://www.rekenwonder.com/atlas.htm V & M Diagrams 15 Foundations Structures F2008abn V & M Diagrams 16 Foundations Structures F2008abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 4

  5. Tools – Visual Analysis (VA Edu) Tools – Visual Analysis (VA Edu) • in open access labs and VOAL and • model view / structure tab https://www.iesweb.com/edu/index.htm – grid and units – define beam members • or pre-defined beams (Create) – select points, assign supports – select members, assign member shapes & any connection types V & M Diagrams 18 Architectural Structures F2018abn V & M Diagrams 17 Architectural Structures F2018abn Lecture 8 ARCH 331 Lecture 8 ARCH 331 Tools – Visual Analysis (VA Edu) • loading tab – select points, add point load – (edit load case with no self weight) • results view – status bar – results filter • member graph – choose options • report view - choose and drag options V & M Diagrams 19 Architectural Structures F2018abn Lecture 8 ARCH 331 5

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