Forging new generations of engineers
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Transcript of Forging new generations of engineers
Forging new generations of engineers
STRUCTURAL ENGINEERING
Structure of a Building
The primary function of a building structure is to support and transmit the loads and forces to the ground.
“Tracing the Loads”or
“Chasing the Loads”
Characteristics of a Structure
Stability – needed to maintain shape. The structure is dependent upon balanced forces and equilibriumStrength - ability of the structure to withstand the applied forces, usually includes a “factor of safety”Economic Value – includes choices made about the design, materials, and function of the structure
Structural Elements
Structural elements in the building consist of: Stringers or Beams Girders Columns Footings Connections
Steps in Structural Design1. Planning – what function will the structure
serve2. Preliminary structural configuration and layout3. Establishing the loads to be carried4. Preliminary sizing of members5. Analysis of structural members6. Evaluate and compare the preliminary design7. Redesign or repeat the above steps as this is
an iterative process8. Designing and detailing the structural
components
Forces and Loads
Design Loads
Dead Loads (DL) – fixed loads building materials or components and the weight of
structural components Given load of building, which is either calculated or is known
Live Loads (LL) – transient and moving loads Occupancy loads and furnishing loads, building usage varies Snow loads Construction loads Live Load maybe variable during structures lifetime Building codes specify Live Loads for floor and roof loadings
Design Loads (continued)Wind Load (WL) –
Depends on Height and location of structure (Exposure categories)
Resulting loads yields: Lateral load on walls Downward and upward
pressure on roofs Overturning of the
structure
WIND
WIND
Pressur
Pressur
eeUplift
Uplift
SuctionSuction
Design Loads (continued)
Earthquake Loads (EQ)
Seismic load based on building mass , type and configuration.
Vertical and lateral forces (dynamic)
Building codes can simplify loading
Seismic Forces at Base of Building
Hypocenter
Epicenter
Design Loads and “Factor of Safety”
Structural Design contains a “factor of safety.” In order to accomplish this, Load Factors are applied to the the various calculated loads. Building Code requirements are conservative in the methods of distribution and the weights of loads, which adds to the “factor of safety.”However, to maintain simplicity we will not use any factored loads for the CEA Project.
Loads & Load Paths
Snow and/or roof load
Use and occupancy load such as DL and LL
Self weight of structure DL
Ground reaction
BEAMS AND COLUMNS
LOADS The building dead load is the only
known load. All other forces will vary in magnitude, duration and location.
The building is designed for design load possibilities that may never occur.
The structural efficiency of a building is measured as the ratio of dead to live load.The building designer strives to keep the ratio low.
Beam Design
Beams are used in floors and roofs.Maybe called floor joists, stringers, floor beams or girders.Loads on beams are either concentrated or uniform loadsBeams are designed for Shear, Moment (bending), and Deflection
Beams
Beams are sized appropriately to safely support the loads a structure will carry.Beams are primarily subjected to bending and shear. Deflection and deformation can be calculated.Beams are sized to provide the maximum result with the minimum materials. A factor of safety is included in the design.
Beam DeflectionLimit Deflection to L/240 of total load (whereas L=length in inches) L/300 of total load L/360 of total load (building use throughout life
is unknown) Preferred Limit
WHY?? Ceiling cracks in plaster Roof ponding (flat roofs) Visual or psychological reasons, such as too
much deflection and people think it could be unsafe
Designer’s judgment
Beam Types
Simple
Continuous
Cantilever Moment
(fixed at one end)
Beam TypesFixed
Moments at each end
Propped- Fixed at one end supported at other
Overhang
Forces and SupportsSupports are translated into forces and moments in a free body diagrams. The following are three common supports and the forces and moments used to replace them.
Roller:
Pin Connection:
Fixed Support:
Fy
Fy
Fx
Fx
Fy
Mo
Columns
Columns carry primary Axial Loads and therefore are designed for compression.Additional loads from snow, wind or other horizontal forces can cause bending in the columns.Columns then need to be designed for Axial Load and Bending.
Column Forces FExternal
WCOL (External
R1 (Internal)
R2 (Internal)
RSoil (External)
WFTG (External)
Horizontal loads caused by wind, snow, seismic or internal building load
LOADS
Building Dead Loads
Weight of the structure (steel, concrete, timber)
Partitions/ WallsDuctworkPipingElectrical fixturesFloor coveringsRoof coveringsCeiling
Typical Building Dead Loads
Concrete (density 150 lb/ft3)per 1 inch thickness 12.5 lb/ft2
Steel and Timber based on structural element weight sPartitions/ Walls— Wood stud 2x4 12” to 16” on center
with ½” gypsum board both sides 6 lb/ft2
— Brick (4” thick) 40 lb/ft2
— Concrete Block (8” Wall) 38 lb/ft2
Typical Building Dead Loads
Floor Covering Tile 12 lb/ft2
Hardwood 4 lb/ft2
Linoleum 1 lb/ft2
Sub floor ¾” plywood 3 lb/ft2
Ceiling Suspended 2 lb/ft2
Drywall 5 lb/ft2
Typical Building Dead Loads
Roofing Sheathing (3/4”) 3 lb/ft2
Asphalt Shingles 3 lb/ft2
Insulation Loose ½ lb/ft2
3 ply ready roofing 1 lb/ft2
5ply felt and gravel 6 lb/ft2
Mechanical Electrical, Ductwork and Plumbing these loads can vary - Estimated 10 lb/ft2
Estimate depends on the type of building Some may use a percentage of Dead Load
Typical Building Uniform Live Loads
Retail First Floor 100 lb/ft2
Upper Floors 80 lb/ft2
Stadiums and Arenas Bleachers 100 lb/ft2
Fixed Seats 60 lb/ft2
Library Stacks 150 lb/ft2
Reading rooms 60 lb/ft2
Offices 50 lb/ft2
Typical Building Uniform Live Loads
Schools Classrooms 40 lb/ft2
First floor corridors 100 lb/ft2
Corridors above first floor 80 lb/ft2
Stadiums and Arenas Bleachers 100 lb/ft2
Fixed Seats 60 lb/ft2
Residential (one and two family) 40 lb/ft2
Hotels and Multifamily Private rooms and corridors 40 lb/ft2
Private rooms and corridors 100 lb/ft2
Snow Load
Snow Load depends on your location. Almost all building codes have Snow Load requirements.Ground Snow Load ( in New York State) Rochester, NY 50 lb/ft2
Albany, NY 55 lb/ft2
Watertown, NY 65 lb/ft2
White Plains, NY 45 lb/ft2
Design for Wind Loads
Dead Loads figure in the evaluation of a building when designing for Wind Load.The building Dead Load can help resist the Overturning and Uplift conditions caused by wind. Typically, a building framed with steel beams and columns will have some type of bracing, such as steel cross bracing or masonry block walls on exterior or in elevator shaft to handle the wind load conditions.The floor slab also helps resist wind loads and shear loads
Building Design
Steel Frame with Concrete Floors and Flat Roof
RETAIL BUILDING
Design notes:
Revit File is for illustrative purposes only. It is a preliminary framing plan and therefore not all steel framing members are accurately noted and resized for final design. Visibility of Wall, Roof, and Slab can be changed to see total framing planNot all walls, slabs, or the roof are shownBuilding left in “Under Construction” stageSteel framed building designed for retail space
FootingColumn
Girder
Beam
Partial View of 2nd floor FramingFor Clarity the Ground Floor Slab, 2nd Floor Slab and Roof Framing and Roof Deck are not shown
3D View of Retail Building
Steel Framing and 1st Floor Slab Shown
Steps in Calculation
1. Analysis of structural members, designing for Moment and checking for Deflection
2. Evaluate and compare to preliminary design3. Redesign or Recalculate as necessary, such
as repeat the above steps as this is an iterative process
4. Calculate Beams loading, transfer loads to Girder, and carry the load to the column and then down to the footing
“Load Chasing” for Structural Design
The structural design is done by “chasing the loads” of the Dead and Live Load though the slabs, to beams, to girders then onto the columns or walls. The loads are then carried down to the footing or foundation walls and then to the earth below.
Chasing Loads for this project
Calculate Beam loading and obtain reactions Transfer reaction loads to GirderCarry the girder reactions to the column and then down to the footing
FOUNDATION PLAN
Partial 2nd FLOOR FRAMING PLAN
Design Area
Beam B.3
Girder 3BC
Tributary or Contributing Area for Beam B.3 is shownPartial 2nd FLOOR FRAMING PLAN
6’-8” Width
Column B-3
Partial Roof FLOOR FRAMING PLAN
Column B-3
Steps for Calculating Beam Loading
1. Find weights of building elements2. Compute weight carried per linear foot of beam
and multiple by Tributary Width3. Assume weight of beam per lineal foot4. Add beam weight to superimposed dead load to
get Total Dead Load (DL) 5. Select Design Live Load (LL) use applicable
building codes 6. Combine DL + LL, this will be the Uniform Load
on Beam, w7. Calculate any Concentrated Loads on Beam
Steps for Calculating Beam Loading continued
8. Use MD Solids to set up Beam Loading and generate the Moment, Shear and End Reactions for the beam
9. Select Member Shape using the Standard Steel Shapes
10. Define Stress Limits (set Steel Yield Stress Fy=36ksi or 50 ksi)
11. Compare Beam Design to Allowable Deflection Limits ( L/360)
12. Select most economical beam ( typically the lightest beam weight)
13. Deflection may control beam size
Beam and Girder Calculations
Second Floor
2nd Floor Loading for Beam B.3 - Dead Load
Span Length 18’-0”Dead Load
4” thick concrete slab 50 lb/ft2
Flooring- Ceramic Tile 10 lb/ft2
Partitions (Drywall with metal stud) 8 lb/ft2
Suspended Ceiling 2 lb/ft2
Mechanical/ Electrical Items 10 lb/ft2
Total DL 80 lb/ft2
Assumed Dead Load Weight of Beam 20 lb/ft
2nd Floor Loading for Beam B.3 - Live Load
Live Load
Retail Space 80 lb/ft2
Total Load DL + LL (per lineal foot of beam) [80lb/ft2 + 80 lb/ft2 ] x 6.67 ft = 1067.2 lb/ft
Add the Beam Weight of 20 lb/ft
Total DL + LL + Beam Weight = 1087.2 lb/ft
Use 1090 lb/ft
Assume: Simple Beam Loading Condition
Span Length is 18 feet.
Uniform Load w = 1090 lb/ft
Uniform Load w= 1090 lb/ft
2nd Floor Loading for Beam B.3
Moment
Shear
Max. Moment = 44,145lb-ft Max. Shear = 9,810 lb
2nd Floor Beam B.3 - Shear and Moment
Design Results for Beam B.3
Note: Beams were sized using MD Solids
By Limiting the Deflection to L /360Where L = 18ft x 12 in/ft = 216 inches
Limit Deflection = L/360 = 216/360 = 0.60 inches
Design Results for Beam B.3
Typically you design for Moment and then check Deflection
Before finishing using MD Solids, use this method that looks at the Moment and Allowable Bending Stress to find out the Required Section Modulus.
Where: SRequired = M/Fb
S is the Section Modulus Required
M is the maximum Moment
Fb is the Allowable Bending Stress
Fb= o.66Fy
For Fy=36,000psi Fb= 24,000 psi
For Fy=50,000psi Fb=33,000 psi
Design Results for Beam B.3
SRequired = M/Fb
M=44,145 ft-lbs
SRequired = (44,145 ft-lb)(12 in/ft) / 24,000 lb/in2
SRequired = 22.07 in3
This is the Required Section Modulus for Beam B.3
Using this value and a reference for Steel Beams, you can select a beam section that fits this requirement.
MD Solids calculates the following :
Standard steel shapes that will be acceptable for the specified bending moment and shear force.
You must select Standard Steel Shapes for the U.S. and use Fy=36,000 psi for Yield Strength of Steel
Design Results for Beam B.3
Selecting Beam Sizes
In selecting wide-flanged structural sections , keep in mind the following:Section Modulus of beam should be large enough so that the Allowable Bending Stress is not exceeded NOTE: MD Solids considered thisLimit Deflection to L/360 where L is in inchesMoment of Inertia of beam should be large enough so that deflection limits are not exceeded, MD Solids calculates the deflection based on the selected structural shape.
Comparisons of the results for Beam B.3
Beam Sz (in4) Deflection (inches)
W10x22 23.2 0.7523
W12x22 25.4 0.5691
W14x22 29.0 0.4461
W10x26 27.9 0.6165
W12x26 33.4 0.4352
W14x26 33.5 0.3624
Limiting Deflection to L/360
This most likely will control the beam design.
SELECT
2nd Floor Loading for Girder 3-BC
Uniform Load w= 50 lb/ft (Estimated weight of Girder)
P1 = P2 =19,620 lb. These are the reactions from each beam similar to Beam B.3 that rest on the Girder
2nd Floor Shear and Moment Girder 3BC
Max. Moment = 133,365 lb-ft Max. Shear = 20,120.0 lb
Design Results for Girder 3BC
The following standard steel shapes will be acceptable for the specified bending moment and shear force.
W16x45 Sz= 72.7 in3 Deflection=0.5773”
W18x46 Sz= 78.8in3 Deflection=0.4761”
Deflection Limit = L/360 = (20 ft x 12 in/ft)/360
Deflection Limit = 0.666”
In MD Solids you should have selected Standard Steel Shapes for the U.S. and used Fy=36,000 psi for Yield Strength of Steel
Roof Calculations for Column Loading
Column B-3
Tributary Roof Area Carried by Column
Column B-3 Loads
We will not size the columns for this project as that is more involved than what we need to do for this CEA project. In addition to the Axial Loads, other loads from snow, wind, or other horizontal forces can cause Bending in columns.Columns are therefore designed for Axial Load and Bending.
Footing Loads for Column B-3
We will size the footing for Column B-3Use Allowable Soil Bearing Capacity = 3000 psfLoads transferred to footing are generated from: Dead and Live Loads from structural
elements above ( 2nd Floor and Roof ) Columns Dead Load ( Self Weight) Loads from 1st Floor slab Dead load of Footing itself
Roof Loads
Dead Load
Roof Type:Corrugated Steel Deck with Insulation and 5 ply Membrane Roof and gravel
Ceiling Suspended 2 lb/ft2
Mechanical Equipment 10 lb/ft2
Steel Deck 5 lb/ft2
Insulation 2 lb/ft2
Roof Membrane and Gravel 6 lb/ft2
Roof Framing 10 lb/ft2
Total 35 lb/ft2
Roof Loads continued
Snow LoadRochester, NY 55 lb/ft2
Total Load on RoofDL + SL = 35 lb/ft2 + 55 lb/ft2 = 90 lb/ft2
This load may seem high, but consider that no additional load was added for Mechanical Roof top equipment
Roof Loads continued
Axial Load On Column B-3 from Roof
Tributary Area of Roof = 18 ft x 20 ft= 360 ft2
DL + SL = 90 lb/ft2
(DL+SL)( Trib. Area)=(90 lb/ft2)(360 ft2)=32,400 lb
Size Footings Under Columns
Loads on Column and Footing
•Loads on Column B-3 have been generated from the Beam and Girder reactions at the Roof , the 2nd Floor
•Additionally, the self weight of the column and footing will also be added to the total load used to Size the Footing
Roof Loads
2nd Floor Loads
1st Floor/ Slab Loads
Soil Bearing Reaction
COLUMN
Column B-3 2nd Floor Partial Plan
Loads on Column and Footing
Loads on the Column
2nd Floor
Girder x 2 = (20,120 lb) 2 = 40,240lb
Beams x 2 = (9,810 lb) 2 = 19,620lb
Roof
Concentrated Load = 32,400 lb
Column Self Weight
21 ft height x 50 lb.ft estimated = 1,050 lb
TOTAL 93,310 lb
USE 94,000 lbs
Loads on Footing
Total Load on Footing = 94,000lb
The Soil is capable of resisting a total bearing pressure of force of 3000 lb/ft2
Using the following formula:
Pressure = Load /Area q= P/A
q = 3000 lb/ft2 is the allowable bearing capacity of the soil
Soil Bearing Capacity Available
Pressure = Load /Area q= P/A
We will need to deduct the weight of the footing, which the footing thickness is 12 inches. This is an estimate, typically standard thickness, but the footing load is high.
(1 ft thick) x 150 lb/ft2 = footing weight in lb/ft2
Weight of Footing = 150 lb/ft2
Soil Capacity Available = 3000 lb/ft2 - 150lb/ft2
Soil Capacity Available = 2850 lb/ft2 = qnet
Sizing the Footing for Column B-3
Soil Capacity Available = 2850 lb/ft2 = qnet
Total Load of Footing = 94,000 lb
Pressure = Load /Area q= P/A
Rearranging the formula so that we can get the required Area of the footing
P/ q net = Area
94,000 lb / 2850 lb/ft2 = 32.98 ft2 = Area Req’d
Footing Size = 5.75 ft X 5.75 ft
USE 6’-0” x 6’-0” Square Footing
Reference Sources
– Jefferis, A., & Madsen, D. A. (2001). Architectural Drafting and Design. Albany, NY: Delmar, a division of Thomson Learning.
– Kane, K., & Onouye, B., (2002). Statics and Strength of Materials for Architecture and Building Construction.(2nd ed.). Saddle River, NJ: Pearson Education, Inc
– Shaeffer, R. E., (2002). Elementary Structures for Architects and Builders (4th ed.). Columbus, OH: Prentice Hall.
– Manual of Steel Construction, (8th ed), American Institute of Steel Construction
– http://www.emporis.com/en/ – http://www.pbs.org/wgbh/buildingbig/lab/forces.html– ASCE Minimum Design Loads for buildings and Other
Structures,ASCE 7-98