ten other beams & pinned frames Continental train platform, - PowerPoint PPT Presentation

E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS S PRING 2019 lecture ten other beams & pinned frames Continental train platform, Grimshaw 1993 Pinned Frames 1 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Continuous Beams • statically indeterminate • reduced moments than simple beam Pinned Frames 2 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Continuous Beams • loading pattern affects – moments & deflection D max Pinned Frames 3 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Continuous Beams • unload end span D max Pinned Frames 4 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Continuous Beams • unload middle span D max Pinned Frames 5 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Moment Redistribution • continuous slabs & beams with uniform loading – joints similar to fixed ends, but can rotate 2 • change in moment to center = wL – M max for simply supported beam 8 Pinned Frames 6 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Moment Distribution (a) • no load http:// nisee.berkeley.edu/godden Pinned Frames 7 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Moment Distribution (b) • add load http:// nisee.berkeley.edu/godden Pinned Frames 8 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Moment Distribution Method (c) • release joint 2 http:// nisee.berkeley.edu/godden Pinned Frames 9 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Moment Distribution Method (d) • release joint 3 http:// nisee.berkeley.edu/godden Pinned Frames 10 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Moment Distribution Method (e) • exposure of final shape after cycles over initial shape http:// nisee.berkeley.edu/godden Pinned Frames 11 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Analysis Methods • Approximate Methods – location of inflection points • Force Method – forces are unknowns • Displacement Method – displacements are unknowns Pinned Frames 12 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Theorem of Three Moments • moments at three adjacent supports (2 spans) • distributed load and same I: 3 3   w L w L       1 1 2 2 2 M L M L L M L 1 1 2 1 2 3 2 4 4 • concentrated loads and same I:       M L 2 M L L M L     1 1 2 1 2 3 2       2 3 2 3 P L n n P L n n 1 1 1 1 2 2 2 2 Pinned Frames 13 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Two Span Beams & Charts • equal spans & symmetrical loading • middle support as flat slope Pinned Frames 14 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Pinned Frames • structures with at least one 3 force body • connected with pins • reactions are equal and opposite – non-rigid – rigid Pinned Frames 15 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Rigid Frames • rigid frames have no pins • frame is all one body • typically statically indeterminate • types – portal – gable Pinned Frames 16 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Rigid Frames with PINS • frame pieces with connecting pins • not necessarily symmetrical Pinned Frames 17 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Internal Pin Connections • statically determinant – 3 equations per body – 2 reactions per pin + support forces B G C E F A D A x A y D Pinned Frames 18 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Arches • ancient • traditional shape to span long distances Pinned Frames 19 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Arches • primarily sees compression • a brick “likes an arch” Pinned Frames 20 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Arches • behavior – thrust related to height to width – funicular: to loading Pinned Frames 21 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Three-Hinged Arch • statically determinant – 2 bodies, 6 equilibrium equations – 4 support, 2 pin reactions (= 6) Pinned Frames 22 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Beams with Internal Pins • statically determinant when – 3 equilibrium equations per link => – 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 23 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614

Procedure • solve for all support forces you can • draw a FBD of each member – pins are integral with member – pins with loads should belong to 3+ force bodies – pin forces are equal and opposite on connecting bodies – identify 2 force bodies vs. 3+ force bodies – use all equilibrium equations Pinned Frames 24 Elements of Architectural Structures S2019abn Lecture 10 ARCH 614