Civil Engineering and Architecture Structural Loads Part 2 Civil Engineering and Architecture Unit 6 Structures

In this lesson: Solve the Building Design Problem “Chase” the Load Calculate Beam and Girder Loading Select the Beam and Girder Size Size the footings

Building Design Problem A Steel Framed Retail Building with Concrete Floors and Flat Roof Please click here to obtain Revit file of the building.

Second Floor Framing Girder Beam Column Footing

Design Steps

Load Chasing for this Problem Calculate beam loading, obtain reactions Transfer reaction loads to girder Carry girder reactions to column then to footing

Foundation Plan

Partial 2nd Floor Framing Plan Design Area

Tributary or Contributing Area 6’8” Width Beam B.3 Column B-3 Girder 3BC

Calculating Beam Loading Please click here to obtain “Steps for Calculating Beam Loading.”

Dead and Live Load Documents Click Here for the Live Load Sheet Click Here for the Dead Load Sheet

2nd Floor Beam, Girder Calculations 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 Beam, Girder Calculations 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

2nd Floor Beam B.3 Calculations MD Solids Span Length is 18 feet. Uniform Load w = 1090 lb/ft

2nd Floor Beam B.3 Calculations MD Solids – Shear and Moment Diagrams Moment Shear

Allowable Bending Stress Allowable Bending Stress = Fb (Yield Strength) Fb = A36 Structural Steel – 36,000 psi (36,000 psi) = 24,000 psi Fb = (50,000 psi) = 33,000 psi Fb =

Section Modulus = M = 44,145 ft-lbs Fb = 24,000 psi = SRequired = 22.073 in3

MDSolids Design Results B.3

Design Results for B.3- con.

Professional Development Lesson ID Code: 8009 Beam B.3 Deflection Deflection limited to: 216 in 360 = 0.6 in Professional Development Lesson ID Code: 8009

Beam B.3 Comparisons Beam Sz (in3) 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 SELECT

Girder 3BC Calculations Beam B.3 Span Length is 18 feet. Uniform Load = 1090 lb/ft P1 = P2 = (18ft)(1090 lb/ft) P1 = P2 = 19,620 lb.

Girder 3BC Moment and Shear

Design Results Deflection Limit = = Deflection Limit = 0.666” Girder Sz (in3) Deflection (inches) W16x45 72.7 0.5773 W18x46 78.8 0.4761

Footing Calculations

Footing Loads Loads Considered Allowable Soil Bearing Capacity = 3000 lb/ft2 Loads Considered Dead & Live load from 2nd floor and roof Column’s weight (dead load) Load from 1st floor slab Dead load from footing

Roof Load Roof Type: Corrugated Steel Deck with insulation and 5 ply membrane roof and gravel, located in Rochester NY. Dead Load Suspended Ceiling 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 DL 35 lb/ft2

Roof Load – Snow Snow Load Rochester, NY 55 lb/ft2 Total Load on Roof DL + SL = 35 lb/ft2 + 55 lb/ft2 = 90 lb/ft2 Axial Load on Column B-3 from Roof Tributary Area of Roof = 18 ft x 20 ft = 360 ft2 (DL + SL)(Trib. Area) = (90 lb/ft2)(360 ft2) = 32,400 lb

Loads on Column and Footing 1st Floor/ Slab Loads Soil Bearing Reaction Roof Loads 2nd Floor Loads Column B-3

Loads on Column - Footing Loads on the Column 2nd Floor Girder x 2 = 2(20,120 lb) = 40,240 lb Beams x 2 = 2(9,810 lb) = 19,620 lb Roof Concentrated Load = 32,400 lb Column Self Weight 21 ft x 50 lb/ft (estimated) = 1,050 lb Total 93,310 lb Use 94,000 lbs

Soil Bearing Capacity Available Allowable Soil Bearing Capacity = 3000 lb/ft2 Footing wt. = (1 ft)(150 lb/ft3) = 150 lb/ft2 Soil Capacity Available = 3000 lb/ft2 - 150lb/ft2 = 2850 lb/ft2 = qnet

Use 6’-0” x 6’-0” Square Footing Sizing the Footing Load Column Footing = 94,000 lbs Soil Capacity Available = 2850 lb/ft2 = qnet Use 6’-0” x 6’-0” Square Footing

The Solutions: Beam B.3 W12x22 Girder B3B W16x45 Footing under Column B-3 6’ x 6’

Curriculum Alignment: Unit 6 – Structural Engineering Lesson 6.1 – Introduction to Structural Engineering Act. 1.1 – Structural Calculations Act. 1.2 – More Load Calculations Lesson 6.2 – Roof Systems Lesson 6.3 – Columns and Beams

References: Jefferis, A. & Madsen, D.A. (2001). Architectural Drafting and Design, Albany, NY: Delmar 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://pbs.org/wgbh/buildingbig/lab/forces.html

Credits: Writer: Constance Bertucci Content Editor: Donna E. Scribner Narration: Donna E. Scribner PLTW Editor: Ed Hughes Production: CJ Amarosa Video Production: CJ Amarosa Audio: CJ Amarosa Project Manager: Donna E. Scribner