A RCHITECTURAL S TRUCTURES : Pinned Frames F ORM, B EHAVIOR, AND D ESIGN ARCH 331 • structures with at least one 3 force body D R. A NNE N ICHOLS • connected with pins S PRING 2018 • reactions are equal and opposite lecture eleven – non-rigid – rigid other beams & pinned frames Continental train platform, Grimshaw 1993 Pinned Frames 1 Architectural Structures F2009abn Pinned Frames 2 Foundations Structures F2008abn Lecture 11 ARCH 331 Lecture 10 ARCH 331 Rigid Frames Rigid Frames with PINS • rigid frames have • frame pieces with no pins connecting pins • frame is all one • not necessarily body symmetrical • typically statically indeterminate • types – portal – gable Pinned Frames 3 Foundations Structures F2008abn Pinned Frames 4 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 1
Internal Pin Connections Arches • ancient • statically determinant • traditional shape to – 3 equations per body – 2 reactions per pin + support forces span long distances B Packhorse Bridge, UK G C E F A D A x A y D Rainbow Bridge National Monument Roman Aquaducts Pinned Frames 6 Foundations Structures F2008abn Pinned Frames 5 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 Arches Arches • primarily sees compression • behavior • a brick “likes an arch” – thrust related to height to width Pinned Frames 7 Foundations Structures F2008abn Pinned Frames 8 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 2
Three-Hinged Arch Compound Beams • statically determinant • statically determinant when – 2 bodies, 6 equilibrium equations – 3 equilibrium equations per link => – 4 support, 2 pin reactions (= 6) – total of support & pin reactions (properly constrained) • zero moment at pins F 2 F 1 F 2 F 1 M R1 R 2x R 1x R 2x (internal) pin R 2y R 2y R 1y R 3 not independent Pinned Frames 9 Foundations Structures F2008abn Pinned Frames 10 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 Procedure Rigid Body Types • solve for all support forces you can • two force bodies • draw a FBD of each member – forces in line, equal and opposite • three force bodies – pins are integral with member – pins with loads should belong to 3+ force – concurrent or parallel forces bodies – pin forces are equal and opposite on F 2 F 2 F 3 F 3 connecting bodies F 1 d 1 B B B C C A d 2 A A – identify 2 force bodies vs. 3+ force bodies F 1 F 2 F 1 – use all equilibrium equations two three three Pinned Frames 11 Foundations Structures F2008abn Pinned Frames 12 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 3
Continuous Beams Continuous Beams • statically indeterminate • loading pattern affects • reduced moments than simple beam – moments & deflection max Pinned Frames 13 Foundations Structures F2008abn Pinned Frames 14 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 Continuous Beams Continuous Beams • unload end span • unload middle span max max Pinned Frames 15 Foundations Structures F2008abn Pinned Frames 16 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 4
Analysis Methods Two Span Beams & Charts • Approximate Methods • equal spans & symmetrical loading – location of inflection points • middle support as flat slope • Force Method – forces are unknowns • Displacement Method – displacements are unknowns Pinned Frames 17 Foundations Structures F2008abn Pinned Frames 18 Foundations Structures F2008abn Lecture 10 ARCH 331 Lecture 10 ARCH 331 5
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