New Methods for Ponding Analysis of Open Web Steel Joist Roofs FEBRUARY 21, 2018

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1 New Methods for Ponding Analysis of Open Web Steel Joist Roofs FEBRUARY 21, 2018 Copyright 2018 Steel Joist Institute. All Rights Reserved. Presented by: Mark D. Denavit, P.E., Ph.D. James M. Fisher, Ph.D., P.E., Dist. M. ASCE

2 Polling Question New requirement to earn PDH credits Two questions will be asked during the duration of today s presentation The question will appear within the polling section of your GoToWebinar Control Panel to respond 2

3 Disclaimer The information presented herein is designed to be used by licensed professional engineers and architects who are competent to make a professional assessment of its accuracy, suitability and applicability. The information presented herein has been developed by the Steel Joist Institute and is produced in accordance with recognized engineering principles. The SJI and its committees have made a concerted effort to present accurate, reliable, and useful information on the design of steel joists and Joist Girders. The presentation of the material contained herein is not intended as a representation or warranty on the part of the Steel Joist Institute. Any person making use of this information does so at one s own risk and assumes all liability arising from such use. 3

4 Learning Objectives 1. Recall the roof ponding requirements within ASCE 7, IBC, and FM Global. 2. Describe the limitations of the method of ponding analysis given in Appendix 2 of the AISC Specification. 3. Investigate the stability of simple roof systems for ponding using the SJI Roof Bay Analysis Tool. 4. Identify the main factors influencing the ponding stability of open-web steel joist roofs. 4

5 New Methods for Ponding Analysis of Open Web Steel Joist Roofs Review of roof ponding requirements and introduction to the SJI Roof Bay Analysis Tool Presented by Jim Fisher The direct analysis method for ponding and using the SJI Roof Bay Analysis Tool to evaluate susceptible bays Presented by Mark Denavit 5

6 Roof Ponding 6

7 SJI Technical Digest No. 3 STRUCTURAL DESIGN OF STEEL JOIST ROOFS TO RESIST PONDING LOADS ORDER FROM steeljoist.org $

8 Roof Ponding Comments on: IBC 2015 ASCE FM Global 1-54, 2016 ANSI/AISC ANSI/SJI

9 International Building Code Roof Drainage. Design and installation of roof drainage systems shall comply with Section 1503 of this code and Sections 1106 and 1108, as applicable, of the International Plumbing Code Secondary (emergency overflow) drains or scuppers. Where roof drains are required, secondary (emergency overflow) roof drains or scuppers shall be provided where the roof perimeter construction extends above the roof in such a manner that water will be entrapped if the primary drains allow buildup for any reason. The installation and sizing of secondary emergency overflow drains, leaders and conductors shall comply with Sections 1106 and 1108, as applicable, of the International Plumbing Code. 9

10 International Building Code Scuppers. When scuppers are used for secondary (emergency overflow) roof drainage, the quantity, size, location and inlet elevation of the scuppers shall be sized to prevent the depth of ponding water from exceeding that for which the roof was designed as determined by Section Scuppers shall not have an opening dimension of less than 4 inches (102 mm). The flow through the primary system shall not be considered when locating and sizing scuppers. 10

11 International Building Code Built-up roofs. The installation of built-up roofs shall comply with the provisions of this section Slope. Built-up roofs shall have a design slope of a minimum of not less than one-fourth unit vertical in 12 units horizontal (2-percent slope) for drainage, except for coal-tar built-up roofs that shall have a design slope of a minimum not less than one-eighth unit vertical in 12 units horizontal (1- percent slope). 11

12 International Building Code Susceptible bays of roofs shall be evaluated for ponding instability in accordance with Section 7.11 of ASCE 7. 12

13 International Building Code Design rain loads. Each portion of a roof shall be designed to sustain the load of rainwater that will accumulate on it if the primary drainage system for that portion is blocked plus the uniform load caused by water that rises above the inlet of the secondary drainage system at its design flow. The design rainfall shall be based on the 100-year hourly rainfall rate indicated in Figure or on other rainfall rates determined from approved local weather data. R = 5.2(d s + d h ) (Equation 16-36) 13

14 International Building Code where: d h = Additional depth of water on the undeflected roof above the inlet of secondary drainage system at its design flow (i.e., the hydraulic head), in inches. d s = Depth of water on the undeflected roof up to the inlet of secondary drainage system when the primary drainage system is blocked (i.e., the static head), in inches. R = Rain load on the undeflected roof, in psf. When the phrase "undeflected roof" is used, deflections from loads (including dead loads) shall not be considered when determining the amount of rain on the roof. 14

15 International Building Code Ponding instability Susceptible bays of roofs shall be evaluated for ponding instability in accordance with Section 8.4 of ASCE Controlled drainage. Roofs equipped with hardware to control the rate of drainage shall be equipped with a secondary drainage system at a higher elevation that limits accumulation of water on the roof above that elevation. Such roofs shall be designed to sustain the load of rainwater that will accumulate on them to the elevation of the secondary drainage system plus the uniform load caused by water that rises above the inlet of the secondary drainage system at its design flow determined from Section Such roofs shall also be checked for ponding instability in accordance with Section

16 ASCE 7-16 Criteria 7.11 Ponding Instability Susceptible bays shall be designed to preclude ponding instability. Roof deflections caused by the full snow loads shall be evaluated when determining the likelihood of ponding instability (see Section 8.4) 16

17 ASCE 7-16 Criteria 8.4 PONDING INSTABILITY AND PONDING LOAD Susceptible bays shall be investigated by structural analysis to assure that they possess adequate stiffness to preclude progressive deflection (i.e., instability) and adequate strength to resist the additional ponding load Any of the following conditions shall be deemed to create susceptible bays: 1) Bays with a roof slope less than 1/4 inch per foot when the secondary members are perpendicular to the free draining edge. 2) Bays with a roof slope less than 1 inch per foot when the secondary members are parallel to the free draining edge. 3) Bays with a roof slope of 1 inch per foot and a span to spacing ratio for the secondary members greater than 16 when the secondary members are parallel to the free draining edge. 4) Bays on which water accumulates (in whole or in part) when the primary drain system is blocked but the secondary drain system is functional. The larger of the snow load or the rain load equal to the design condition for a blocked primary drain system shall be used in this analysis. 17

18 Susceptible bays- ASCE 7 18

19 FM Global 1-54 SECTION A. Provide secondary drainage to prevent any possibility of rain water overload. The overflow relief provision establishes the maximum possible water level based on blockage of the primary drainage system. Ensure the provision is in the form of minimal height roof edges, slots in roof edges, overflow scuppers in parapets or overflow drains adjacent to primary drains. B. Ensure the overflow relief protection provides positive and uniform drainage relief for each roof section. C. When designing and sizing the secondary drainage system (overflow drains or scuppers), assume the primary drains are 100% blocked and cannot flow water. D. Ensure the inlet elevation of overflow drains and the invert elevation (see sketches in Table 6a and 8d) of overflow scuppers are not less than 2 in. (50 mm) nor more than 3 in. (75 mm) above the low point of the (adjacent) roof surface unless a safer water depth loading, including the required hydraulic head to maintain flow, has been determined by the roof-framing designer. 19

20 AISC Specifications- Section B3 DESIGN BASIS B3.10. Design for Ponding The roof system shall be investigated through structural analysis to ensure strength and stability under ponding conditions, unless the roof surface is configured to prevent the accumulation of water. Methods of evaluating stability and strength under ponding conditions are provided in Appendix 2. 20

21 AISC Appendix 2 This appendix provides methods for determining whether a roof system has adequate strength and stiffness to resist ponding. These methods are valid for flat roofs with rectangular bays where the beams are uniformly spaced and the girders are considered to be uniformly loaded. The appendix is organized as follows: 2.1. Simplified Design for Ponding 2.2. Improved Design for Ponding The members of a roof system shall be considered to have adequate strength and stiffness against ponding by satisfying the requirements of Sections 2.1 or

22 AISC Appendix SIMPLIFIED DESIGN FOR PONDING The roof system shall be considered stable for ponding and no further investigation is needed if both of the following two conditions are met: C p + 0.9C s 0.25 I d 25(S 4 )10-6 I d 3940S 4 (A-2-1) (A-2-2) (A-2-2M) 22

23 AISC Appendix IMPROVED DESIGN FOR PONDING It is permitted to use the provisions in this section when a more accurate evaluation of framing stiffness is needed than that given by Equations A-2-1 and A-2-2. Define the stress indexes U p 08. Fy fo = fo p for primary member (A-2-5) U s 08. Fy fo = fo s for secondary member (A-2-6) 23

24 AISC SPECIFICATION Improved Design: U U p s 0.8Fy fo = f o 0.8Fy = fo f o p s for the primary member (Eq. A-2-5) for the secondary member (Eq. A-2-6) U p, the stress index for the primary member U s, the stress index for the secondary member C p, the stiffness index for the primary member C s, the stiffness index for the secondary member f o, the stress at initiation of ponding 24

25 AISC Appendix 2 Ponding Assumptions Framing is flat. Members are not cambered. Tapered insulation not considered. Bays are rectangular. Adjacent bays are identical. Beams are uniformly spaced. All beams have equal stiffness. All members are simply supported. Axial loads not present. Water load covers the entire bay. 25

26 Ponding Load Strategies based on the AISC provisions: Provide roof systems to avoid ponding by sloping roof members, or by the use of tapered insulation or sloping fill. Stiffen the roof s structural members by selecting a combination of low flexibility constants which satisfy Equation A-2-1 of the AISC Specification Appendix 2 (AISC 2016). Conduct a more exact analysis for ponding following the procedures given in the AISC Specification Appendix 2. Counteract the ponding mechanism by providing upward camber in the joists, provided that drains are installed near columns (see FM Global 1-54 FM (2016). When designing roofs with low slopes, parallel chord joists with end supports at different elevations are more economical than providing pitch into the joist top chords. The web system of a non-parallel chord joist and the joist as a whole is more expensive to manufacture 26

27 ANSI/SJI Standard Specification for K-Series, LH-Series, and DLH- Series Open Web Steel Joists and for Joist Girders. The SJI Specifications in Section 5.11 contains the following requirement relative to ponding: The ponding investigation shall be performed by the specifying professional. 27

28 COMMENTS ON THE CITED DOCUMENTS: All roofs require a secondary drainage system. All roofs must be designed for impounded water based on the primary drains being blocked. Impounded water heights are to include the hydraulic head above the secondary drainage system. Ponding instability checks are to be made using the larger of snow load or rain load (impounded water). 28

29 COMMENTS ON THE CITED DOCUMENTS: For roofs with snow loads of 20 psf or less, an additional 5 psf of rain on snow must be used in design. Follow IBC requirements in Section Slope. Built-up roofs shall have a design slope of not less than one-fourth unit vertical in 12 units horizontal (2-percent slope) for drainage, except for coal-tar built-up roofs that shall have a design slope of not less than one-eighth unit vertical in 12 units horizontal (1-percent slope). 29

30 Roof Ponding- Maintenance 30

31 Roof Ponding- Construction 31

32 Roof Ponding- Unique Geometry 32

33 Roof Ponding- Unique Geometry Water Flow Slope Typical Drain Parapet 33

34 SJI Roof Bay Analysis Tool 34

35 Free download available for SJI spreadsheet tools. 35

36 SJI Roof Bay Analysis Tool 36

37 General Info Tab Copyright

38 General Info Tab- ASD or LRFD 38

39 General Info Tab - Notes Governing code is IBC Bay sizes are limited to Joist and Joist Girder Load Tables. Deck size selected by minimum weight and deflection limits, from SDI Tables. Deck deflection is based on minimum of I p or I n, per direction of SDI. SDI minimum bearing lengths assumed. Joist size selected by minimum weight and deflection limits from SJI Load Tables. DLH joist data is limited to spans greater than the safe load spans in the SJI Load Tables. 39

40 SJI Roof Bay Analysis Tool 40

41 Load Input New in Version

42 Steel Deck and Joist Spacing Input 42

43 Joist /Joist Girder Depths & Deflection Checks Suggest doing this. OPTIONAL INCREASED LOAD DATA Member I I eff = I/1.15 Joist Load lb / ft 18K in. 4 JG Panel Point Load kips 60G10N4.6F in. 4 NEW 43

44 Design Summaries 44

45 Cost Data Input 45

46 Cost & Design Summary 46

47 Run Data Summary 47

48 Run Comparisons 48

49 Polling Question Which of the following is NOT one of the assumptions made for the ponding provisions in Appendix 2 of the AISC Specification? A. The roof satisfies the IBC minimum slope requirements. B. The members are not cambered. C. The beams are uniformly spaced. D. The beams have equal stiffness. E. Water load covers the entire bay. 49

50 New Methods for Ponding Analysis of Open Web Steel Joist Roofs Review of roof ponding requirements and introduction to the SJI Roof Bay Analysis Tool Presented by Jim Fisher The direct analysis method for ponding and using the SJI Roof Bay Analysis Tool to evaluate susceptible bays Presented by Mark Denavit 50

51 Limitations of the AISC Appendix 2 Method Flat roof construction The method in AISC Appendix 2 assumes a perfectly flat roof No roof slope and no camber Moment and shear envelopes The method in AISC Appendix 2 checks only the maximum moment No check for moment and shear strength that vary along the length No local checks (e.g., bending between panel points) Level of loading The method in AISC Appendix 2 is only intended for use with ASD No provisions for use with LRFD 51

52 Direct Analysis Method for Ponding A new method to evaluate roofs for ponding Similar in concept to the direct analysis method described in Chapter C of the AISC Specification, but there are many differences Load-effects due to impounded water are computed directly based on the deformed shape of the roof system Check performed by comparing required strengths to available strengths 52

53 Required Strengths Determined from an analysis that captures the nonlinear loading from the impounded water Closed-form solutions available for simple cases Iterative analysis for general cases Geometric nonlinearity (second-order effects) and material nonlinearity (inelasticity) need not be captured 53

54 Load Combinations For the ponding check SJI recommends using: D P S for ASD 1.2D + 1.2P + 1.2S for LRFD Note that the IBC strength combinations still need to be checked D + (L r or S or R) for ASD 1.2D + 1.6(L r or S or R) for LRFD D = Dead Load P = Impounded Water Load S = Snow Load L r = Roof Live Load 54 R = Rain Load

55 Force Level Adjustment Factor Requirement from Chapter C of the AISC Specification: All load-dependent effects shall be calculated at a level of loading corresponding to LRFD load combinations or 1.6 times ASD load combinations. For design by ASD, the analysis is conducted under 1.6 times the ASD load combination, and the resulting internal forces are divided by 1.6 to obtain the required strengths of components 55

56 Loads Water and snow act at the same time, but account for the physical overlap of material Density of water only = 62.4 lb/ft 3 Density of snow only = γ (14-30 lb/ft 3, ASCE 7-16 Equation 7.7-1) Density of water and snow = 62.4 lb/ft 3 Water Level Water Only 56

57 Available Strengths Moment and shear envelopes per the SJI Specification wl 2 /8 wl/2 0 wl/8 (25% of end reaction, per SJI Specification) wl/16 (12.5% of end reaction, assumed) 0 Shear diagram for simply supported beam under uniformly distributed load -wl/2 Joist Moment Envelope Joist Shear Envelope Note that the SJI Specification does not require any strength for shear reversals. 12.5% of end reaction is assumed and action must be taken to ensure that capacity 57

58 Available Strengths Moment and shear envelopes per the SJI Specification M max R R/4 (25% of end reaction, per SJI Specification) 25% of shear envelope in reverse direction per SJI Specification 0 0 Shear diagram for simply supported beam with equal point loads R Joist Girder Moment Envelope Joist Girder Shear Envelope 58

59 SJI Roof Bay Analysis Tool These sheets allow you to check a bay for ponding New in Version

60 General Input General data referenced from Roof Bay Analysis sheet General Input (Defined in Roof Bay Analysis Spreadsheet) Design Methodology Joist Span Joist Girder Span Joist Size Joist Allowable Load Joist Girder Size Joist Girder Allowable Load Number of Joist Spaces Dead Load on Joists Joist Girder Self Weight Snow Load ASD ft ft 24K lb/ft 36G8N6.2K 6.2 k psf lb/ft psf 60

61 Ponding Specific Input Ponding Specific Input Additional data beyond what is defined on the Roof Bay Analysis sheet Defines: Water load Load factors Undeformed shape of the roof (slope and camber) Adjacent bays etc. Water level relative to zero datum: in Compute load on deformed roof: Y (Y or N) Snow density: lb/ft 3 Force level adjustment factor (α): 1.60 override: Load factors: Dead 1.00 override: Snow 0.75 override: Ponded Water 0.75 override: Top of roof elevation: Top Left in Top Right in Bottom Left in Bottom Right in Camber: Joist in override: in Top Joist Girder in override: in Bottom Joist Girder in override: in Bay is mirrored: Left Y (Y or N) Right Y (Y or N) Top N (Y or N) Bottom Y (Y or N) Joist support is wall: Top Bottom Joist is rigid: Joist 1 (Leftmost) Joist 9 (Rightmost) Effective moment of inertia: Joist in 4 (Values include override: in factor for Joist Girder 1,677 in 4 shear deformations) override: in 4 Y (Y or N) N (Y or N) N (Y or N) N (Y or N) 61

62 Analysis Procedure Read input and set up analysis (e.g., compute joist and joist girder stiffness matrices) Loop until convergence: Compute ponded water loads Analyze each joist Analyze joist girders (if necessary) Check for convergence based on ponded water load vector Compute and display and moments, shears, and equivalent loads RUN ANALYSIS Iteration ΣW # (kips) Convergence! 62

63 Computing Ponding Loads The bay discretized into a grid of cells to compute ponding loads. Further subdivision into a 4x4 gird within each cell Colombi, P. (2006). The Ponding Problem on Flat Steel Roof Grids. Journal of Constructional Steel Research, 62(7),

64 Joist Output Joist Output RUN ANALYSIS Joist Max Shear Equiv. Load Max Moment Equiv. Load Strength Strength Number kips lb/ft kip-ft lb/ft Ratio Check OKAY OKAY OKAY OKAY OKAY OKAY OKAY OKAY OKAY NOTES: 1. Loads and load effects correspond to ASD load combinations. 2. Strength ratio computed assuming shear capacity equal to 12.5% of the end reaction for shear reversals, see Note 14 on the Ponding Instructions spreadsheet. 64

65 Joist Output Joist Total Distributed Load on Joist as a Function of Distance from Bottom Support (lb/ft) Number 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0" NOTES: 1. Loads correspond to ASD load combinations. 2. Highlighted distributed loads may cause a local overstress, see notes on Ponding Instructions spreadsheet. 65

66 Joist Output Joist Total Distributed Load in Excess of Allowable Load on Joist as a Function of Distance from Bottom Support (lb/ft) Number 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0"

67 Joist Girder Output Joist Girder Output Joist Girder size can be revised by inputting larger loads in the ''optional increased load data'' section of the Roof Bay Analysis spreadsheet Top Joist Girder Joist Joist React. Panel Point Load Joist React. Number kips kips kips Bottom Joist Girder Panel Point Load kips Equiv. Load for Shear (kips): N/A (WALL) Equiv. Load for Shear (kips): 9.78 Equiv. Load for Moment (kips): N/A (WALL) Equiv. Load for Moment (kips): 9.62 Strength Ratio: N/A (WALL) Strength Ratio: 1.58 Strength Check: N/A (WALL) Strength Check: NO GOOD NOTES: 1. Loads and load effects correspond to ASD load combinations. 2. Highlighted panel point loads may cause a local overstress, see notes in Ponding Instructions. 67

68 Procedure 1. Complete initial design of roof system for primary design loads and identify susceptible bays in accordance with Section 8.4 of ASCE The remaining steps will need to be completed for each unique susceptible bay. 2. Determine the joist and Joist Girder preliminary design using the roof bay analysis spreadsheet. 3. Determine the hydraulic head based on the flow rate, Q, and the drainage system. The flow rate can be determined using ASCE 7-16 Equation C8-1. The hydraulic head can be determined based on ASCE 7-16 Table C8.3-1 (overflow dams or standpipes), C8.3-3 (scuppers), or C8.3-5 (circular scuppers) 68

69 Procedure 4. Determine the water level above the primary drain (d h + d s ). Check the Building Code to see if a minimum height for secondary drains is provided. ASCE 7-16 provides no minimum height except that the height should be higher than the primary drain. A minimum of 2 inches above the primary drain is often used and is required by FM Global. Some codes require that scuppers be a minimum of 2 inches above the roof level, but should not exceed 4 inches above the roof level. 5. Input the required data into the ponding analysis spreadsheet. The data from the roof bay analysis is automatically transferred to the ponding analysis. 69

70 Procedure 6. Run the ponding analysis. If stability is achieved, the analysis is complete. Ponding stability is achieved when the shear and moment envelopes for the joists and Joist Girders are not exceeded. If stability is not achieved, return to the roof bay analysis and select a larger joist, Joist Girder, or both by inputting increased loads in the optional increased load data section (or decrease the joist spacing). Rerun the ponding analysis until stability is achieved. If local load effects are indicated (loads highlighted with red font) determine based on analysis or judgement whether the indicated applied loads will cause a localized overstress. If the loads are determined to cause overstress, rerun the analysis with larger joists or Joist Girders. 70

71 Procedure 7. Determine if loading on the joists is symmetric or could cause shear reversals. If there is potential for shear reversal in the joists and shear reversal is not addressed via other design loading criteria such as Net Uplift or Snow Drift, specify that joist manufacturer is required to design joists and Joist Girder webs for a minimum vertical shear equal to 12.5% of the end reaction in compression. wl/2 wl/8 (25% of end reaction, per SJI Specification) wl/16 (12.5% of end reaction, assumed) 0 Shear diagram for simply supported beam under uniformly distributed load -wl/2 71

72 Example Example 2 from SJI Technical Digest 3 Controlling susceptible bay Structure located in Memphis, TN Drain Elevation = -10 in. Overflow Scupper Elevation = -8 in. Secondary drains are 24 in. wide open channel scuppers 72

73 Project Description and Loading Girder Length, L g = 40 ft Girder Depth = 36 in. Number of Girder Top Chord Panel Point Spaces, N = 8 Joist Length, L j = 40 ft Joist Spacing, S = 5 ft Dead Load, w D = 18 psf Girder Dead Load, w D = 1 psf Live Load, w L = 20 psf (reducible) Snow Load, w s = 7 psf (requires 5 psf rain-on-snow surcharge load; see IBC and Section 7.10 of ASCE 7-16) 73

74 Preliminary Design Enter the relevant data into the Roof Bay Analysis sheet Set maximum Joist Girder depth to 36 in. Data automatically transferred to the Ponding Analysis sheet Design satisfactory for dead, live, and snow loads Still need to check rain load combination and ponding stability General Input (Defined in Roof Bay Analysis Spreadsheet) Design Methodology Joist Span Joist Girder Span Joist Size Joist Allowable Load Joist Girder Size Joist Girder Allowable Load Number of Joist Spaces Dead Load on Joists Joist Girder Self Weight Snow Load ASD ft ft 24K lb/ft 36G8N6.2K 6.2 k psf lb/ft psf 74

75 Determine Hydraulic Head There are two overflow suppers, each has a tributary area of half the total area of the roof: A = (60 ft.)(80 ft.) = 4800 ft. 2 The 100-year hourly rainfall rate for Memphis, TN is 3.75 in./hr. as determined from Figure in the 2015 IBC i = 3.75 in./hr 75

76 Determine Hydraulic Head Determine the flow rate using Equation C8-1 in ASCE 7-16: Q = Ai, gals/min. (ASCE 7-16 Eq. C8.3-1) Q = (0.0104)(4800 ft. 2 )(3.75 in./hr) = gals/min. 76

77 Determine Hydraulic Head A flow rate of gals/min. corresponds to a hydraulic head between 1 and 2 in. for the 24 in. wide scupper according to Table C8.3-3 of ASCE Interpolating yields d h = 1.9 in. Use d h = 2 in. 77

78 Determine Snow Density The ground snow load for Memphis, TN is 10 psf as determined from Figure of ASCE 7-16 p g = 10 psf Determine the snow density using Equation of ASCE 7-16 γ = 0.13p g lb/ft 3 γ = 15.3 lb/ft 3 78

79 Ponding Specific Input Water level 2 in. above secondary drain -8 in. + 2 in. = -6 in. Compute load on deformed roof: Yes SJI Recommended Load Combination D P S α = 1.6 Ponding Specific Input Water level relative to zero datum: in Compute load on deformed roof: Y (Y or N) Snow density: lb/ft 3 Force level adjustment factor (α): 1.60 override: Load factors: Dead 1.00 override: Snow 0.75 override: Ponded Water 0.75 override: Top of roof elevation: Top Left in Top Right in Bottom Left in Bottom Right in Camber: Joist in override: in Top Joist Girder in override: in Bottom Joist Girder in override: in Bay is mirrored: Left Y (Y or N) Right Y (Y or N) Top N (Y or N) Bottom Y (Y or N) Joist support is wall: Top Bottom Joist is rigid: Joist 1 (Leftmost) Joist 9 (Rightmost) Effective moment of inertia: Joist in 4 (Values include override: in factor for Joist Girder 1,677 in 4 shear deformations) override: in 4 Y (Y or N) N (Y or N) N (Y or N) N (Y or N) 79

80 Joist Output Joist Output RUN ANALYSIS Joist Max Shear Equiv. Load Max Moment Equiv. Load Strength Strength Number kips lb/ft kip-ft lb/ft Ratio Check OKAY OKAY OKAY OKAY OKAY OKAY OKAY OKAY OKAY NOTES: 1. Loads and load effects correspond to ASD load combinations. 2. Strength ratio computed assuming shear capacity equal to 12.5% of the end reaction for shear reversals, see Note 14 on the Ponding Instructions spreadsheet. 80

81 Joist Output Joist Total Distributed Load on Joist as a Function of Distance from Bottom Support (lb/ft) Number 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0" Applied loads greatest at location of greatest deflection Constant applied load where the roof is above the water level NOTES: 1. Loads correspond to ASD load combinations. 81

82 Joist Girder Output Joist Girder Output Joist Girder size can be revised by inputting larger loads in the ''optional increased load data'' section of the Roof Bay Analysis spreadsheet Top Joist Girder Joist Joist React. Panel Point Load Joist React. Number kips kips kips Bottom Joist Girder Panel Point Load kips Equiv. Load for Shear (kips): N/A (WALL) Equiv. Load for Shear (kips): 7.58 Equiv. Load for Moment (kips): N/A (WALL) Equiv. Load for Moment (kips): 7.47 Strength Ratio: N/A (WALL) Strength Ratio: 1.22 Strength Check: N/A (WALL) Strength Check: NO GOOD NOTES: 1. Loads and load effects correspond to ASD load combinations. 2. Highlighted panel point loads may cause a local overstress, see notes in Ponding Instructions. 82

83 Revise Design The 36G8N6.2K which was selected by the roof bay analysis sheet based on dead, live, and snow loading is insufficient for the ponding condition. It needs to be strengthened or stiffened. The Joist Girder will be both strengthened and stiffened if the panel point load is increased. OPTIONAL INCREASED LOAD DATA Member I I eff = I/1.15 Joist Load lb / ft 24K in. 4 JG Panel Point Load 7.5 kips 36G8N7.5K in. 4 Revise the design to 36G8N7.5K using the optional increased load data in the roof bay analysis sheet 83

84 Joist Girder Output Joist Girder Output Top Joist Girder Joist Joist React. Panel Point Load Joist React. Number kips kips kips Bottom Joist Girder Panel Point Load kips Equiv. Load for Shear (kips): N/A (WALL) Equiv. Load for Shear (kips): 7.37 Equiv. Load for Moment (kips): N/A (WALL) Equiv. Load for Moment (kips): 7.29 Strength Ratio: N/A (WALL) Strength Ratio: 0.98 Strength Check: N/A (WALL) Strength Check: OKAY NOTES: 1. Loads and load effects correspond to ASD load combinations. 84

85 Check IBC Strength Load Combination Differences in ponding specific input Compute load on deformed roof: No Load factors (D + R) Bay found to be adequate Ponding Specific Input Water level relative to zero datum: in Compute load on deformed roof: N (Y or N) Snow density: lb/ft 3 Force level adjustment factor (α): 1.60 override: Load factors: Dead 1.00 override: Snow 0.00 override: Ponded Water 1.00 override: Top of roof elevation: Top Left in Top Right in Bottom Left in Bottom Right in Camber: Joist in override: in Top Joist Girder in override: in Bottom Joist Girder in override: in Bay is mirrored: Left Y (Y or N) Right Y (Y or N) Top N (Y or N) Bottom Y (Y or N) Joist support is wall: Top Bottom Joist is rigid: Joist 1 (Leftmost) Joist 9 (Rightmost) Effective moment of inertia: Joist in 4 (Values include override: in factor for Joist Girder 1,677 in 4 shear deformations) override: in 4 Y (Y or N) N (Y or N) N (Y or N) N (Y or N) 85

86 Example Example 4 from SJI Technical Digest 3 Determine if the roof is free draining under the total superimposed loads Dead Load = 14 psf Dead Load = 1 psf (Joist Girder) Snow Load = 25 psf Do not consider camber Due to wall attachment assume the edge joist does not deflect. The roof has a slope of 1/4 in./ft. downward to the right. 86

87 Preliminary Design Use the roof bay analysis tab to design the bay for dead and snow load 26K6 Joist 56G8N10K Joist Girder General Input (Defined in Roof Bay Analysis Spreadsheet) Design Methodology Joist Span Joist Girder Span Joist Size Joist Allowable Load Joist Girder Size Joist Girder Allowable Load Number of Joist Spaces Dead Load on Joists Joist Girder Self Weight Snow Load ASD ft ft 26K lb/ft 56G8N10K 10 k psf lb/ft psf 87

88 Ponding Specific Input Set water level as elevation of edge joist Override load factors to a nominal load condition for this serviceability check D + P + S α = 1.0 Override camber to zero (per problem statement) Ponding Specific Input Water level relative to zero datum: 0.00 in Compute load on deformed roof: Y (Y or N) Snow density: 0.00 lb/ft 3 Force level adjustment factor (α): 1.00 override: 1.00 Load factors: Dead 1.00 override: Snow 1.00 override: 1.00 Ponded Water 1.00 override: 1.00 Top of roof elevation: Top Left in Top Right in Bottom Left in Bottom Right in Camber: Joist in override: 0 in Top Joist Girder in override: 0 in Bottom Joist Girder in override: 0 in Bay is mirrored: Left Y (Y or N) Right N (Y or N) Top Y (Y or N) Bottom Y (Y or N) Joist support is wall: Top Bottom Joist is rigid: Joist 1 (Leftmost) Joist 9 (Rightmost) Effective moment of inertia: Joist in 4 (Values include override: in factor for Joist Girder 5,259 in 4 shear deformations) override: in 4 N (Y or N) N (Y or N) N (Y or N) Y (Y or N) 88

89 Output Iteration ΣW # (kips) Converges with water Joist Total Distributed Load on Joist as a Function of Distance from Bottom Support (lb/ft) Number 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0" THE ROOF IS NOT FREE DRAINING Water present on first two upslope joists as indicated by load > 244 lb/ft NOTES: 1. Loads correspond to ASD load combinations. 2. Highlighted distributed loads may cause a local overstress, see notes on Ponding Instructions spreadsheet. 89

90 Ponding Specific Input Revise design by increasing the size of the joist Determine the required moment of inertia by trial and error Ponding Specific Input Water level relative to zero datum: 0.00 in Compute load on deformed roof: Y (Y or N) Snow density: 0.00 lb/ft 3 Force level adjustment factor (α): 1.00 override: 1.00 Load factors: Dead 1.00 override: Snow 1.00 override: 1.00 Ponded Water 1.00 override: 1.00 Top of roof elevation: Top Left in Top Right in Bottom Left in Bottom Right in Camber: Joist in override: 0 in Top Joist Girder in override: 0 in Bottom Joist Girder in override: 0 in Bay is mirrored: Left Y (Y or N) Right N (Y or N) Top Y (Y or N) Bottom Y (Y or N) Joist support is wall: Top Bottom Joist is rigid: Joist 1 (Leftmost) Joist 9 (Rightmost) Effective moment of inertia: Joist in 4 (Values include override: 485 in factor for Joist Girder 5,259 in 4 shear deformations) override: in 4 N (Y or N) N (Y or N) N (Y or N) Y (Y or N) 90

91 Output Iteration ΣW # (kips) Converges without water Joist Total Distributed Load on Joist as a Function of Distance from Bottom Support (lb/ft) Number 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0" THE ROOF IS FREE DRAINING Select a joist with I e 485 in 4 Uniform total load indicates no impounded water present NOTES: 1. Loads correspond to ASD load combinations. 91

92 Summary and Conclusions Provisions related to ponding exist in several codes The commonly used AISC Appendix 2 method for evaluating ponding has several limitations, especially for open-web steel joist roofs A new method, direct analysis for ponding, has been developed and implemented within the SJI Roof Bay Analysis Tool The recently updated SJI Technical Digest 3 provides additional background information and details. 92

93 Polling Question Which of the following statements is NOT true for ponding evaluation using the SJI Roof Bay Analysis Tool? A. Joists and Joist Girders can be sloped. B. Joists and Joist Girders can be cambered. C. Spacing between joists does not have to be equal. D. Loads on joists and Joist Girders can be calculated on undeformed roofs. E. ASD and LRFD solutions are possible. 93

94 Polling Question Answers Which of the following is NOT one of the assumptions made for the ponding provisions in Appendix 2 of the AISC Specification? A. The roof is assumed to be flat Which of the following statements is NOT true for ponding evaluation using the SJI Roof Bay Analysis Tool? The roof satisfies the IBC minimum slope requirements. C. The SJI Roof Bay Analysis Tool can only model uniformly spaced joists. 94

95 THANK YOU Copyright 2018 Steel Joist Institute. All Rights Reserved. Presented by: Mark D. Denavit, P.E., Ph.D. James M. Fisher, Ph.D., P.E., Dist. M. ASCE 95