four design methods & beams APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2018 lecture STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631

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1 APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2018 lecture four design methods & beams Forum, Pompeii Methods & Beams 1

2 Allowable Stress Design historical method a.k.a. working stress, stress design stresses stay in ELASTIC range Methods & Beams 2

3 Allowable Stress Design codes wood National Design Specification Manual of Timber Construction (glulam) masonry Masonry Specification Joint Code steel Steel Joist Institute American Institute of Steel Construction Methods & Beams 3

4 Limit State Design stresses go to limit (strain outside elastic range) loads may be factored resistance or capacity reduced by a factor based on material behavior state of the art Methods & Beams 4

5 Limit State Design codes wood National Design Specification masonry Masonry Specification Joint Code concrete American Concrete Institute Precast & Prestressed Concrete steel Methods & Beams 5 Steel Joist Institute American Institute of Steel Construction

6 Reinforced Concrete Design ultimate strength design factor applied to capacity different for flexure, shear, bearing... factors applied to loads (ASCE 7) may be different for combinations U 1. 2D 1. 6L U 1. 2D 1. 0W 1. 0L can use alternate values & factors (older codes) Methods & Beams 6

7 Reinforced Concrete Design want steel to yield first ductile failure underreinforced find flexure capacity or resistance from ultimate stresses in steel uniform stress block in concrete Methods & Beams 7

8 Reinforced Concrete Design Methods & Beams 8

9 Steel Design load and resistance factor design like concrete, but capacity related to material R u combinations, ex: 1.4D 1.2D + 1.6L compression capacity load factors load types R c P n u R n 0.85 A g nominal strength resistance factor F cr Methods & Beams 9

10 Plastic Design bending & beams all of material sees ultimate stress refers primarily to steel behavior statically indeterminate systems Methods & Beams 10

11 Elastic vs. Plastic Behavior Hooke s law valid f E yield point is end of elastic range for a ductile material f continued strain with no more load f y = 50ksi 1 E y = Methods & Beams 11

12 Internal Moments - ALL at yield all parts reach yield plastic hinge forms ultimate moment A tension = A compression M u l t or M p bc 2 f y 3 2 M y Methods & Beams 12

13 Plastic Hinge Development Methods & Beams 13

14 Plastic Hinge Examples stability can be effected Methods & Beams 14

15 Plastic Section Modulus shape factor, k = 3/2 for a rectangle k M p M y 1.1 for an I k Z S plastic modulus, Z Z M f y p Methods & Beams 15

16 Beams transverse loading sees: bending shear deflection torsion bearing cross section shape Methods & Beams 16

17 Beams maximum stress distribution principal stresses resultant of shear and bending stress Methods & Beams 17

18 Beams deflections 2 d dx y 2 curv ature M ( x EI ) Methods & Beams 18 U.Washington ENGR 220

19 Beams design: bending stress not exceeding allowable or limit stress F allowable f b Mc I S req' d M F all Methods & Beams 19

20 Beams bending stresses dominate shear stresses exist horizontally with shear no shear stresses with pure bending Methods & Beams 20

21 Beams V & M drawings help determine M max V + V ( w ) dx - M + M ( V ) dx inflection points where slope of M=0 L Methods & Beams 21

22 Beams prismatic (constant cross section) maximum stress maximum moment non-prismatic S varies + M + L Methods & Beams 22

23 Beam Design 1. Know F allowable for the material or f u for LRFD 2. Draw V & M, finding M max h 3. Calculate S req d 4. Determine section size S b bh 6 2 Methods & Beams 23

24 Beam Design 4*. Include self weight for M max 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 Methods & Beams 24

25 Beam Design 5. Consider lateral stability (cont) lateral buckling caused by compressive forces at top couples with insufficient rigidity can occur at low stress levels stiffen or brace Methods & Beams 25

26 Beam Design 6. Evaluate shear stresses - horizontal W and rectangles max 3V 2 A V A web Methods & Beams 26

27 Beam Design 6. Evaluate shear stresses (cont) thin walled open or closed ave VQ Ib q VQ I Methods & Beams 27

28 Beam Design 7. Provide adequate bearing area at supports P 8. Evaluate torsion T T cross section Methods & Beams 28 + L T f p A τ Tρ J

29 Beam Design 8. Torsion (cont) round-ish τ J rectangular τ max Tρ J 1 π c 2 T c 1 ab 4 2 Methods & Beams 29

30 Beam Design 8. Torsion (cont) open long sections τ m ax T 1 ab 3 2 Methods & Beams 30

31 Beam Design 9. Evaluate deflections y max & location Methods & Beams 31

32 Deflection Limits based on service condition, severity Use LL only DL+LL Roof beams: Industrial L/180 L/120 Commercial plaster ceiling L/240 L/180 no plaster L/360 L/240 Floor beams: Ordinary Usage L/360 L/240 Roof or floor (damageable elements) L/480 Methods & Beams 32

33 Continuous Beams statically indeterminate reduced moments than simple beam Methods & Beams 33

34 Continuous Beams loading pattern affects moments & deflection D max Methods & Beams 34

35 Continuous Beams unload end span D max Methods & Beams 35

36 Continuous Beams unload middle span D max Methods & Beams 36

37 Beam Materials timber glu-lam wood concrete steel reinforced masonry Methods & Beams 37 nisee.berkeley.edu/godden

38 Tools Multiframe in classrooms and open access labs Methods & Beams 38

39 Tools Multiframe frame window define beam members select points, assign supports select members, assign section load window select point or member, add point or distributed loads Methods & Beams 39

40 Tools Multiframe to run analysis choose Analyze menu plot Linear choose options double click (all) results choose options Methods & Beams 40