Beam Design. Stress Axial Stress Strain Factor of Safety Bending Stress Shear Stress Beam Selection...
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Transcript of Beam Design. Stress Axial Stress Strain Factor of Safety Bending Stress Shear Stress Beam Selection...
![Page 1: Beam Design. Stress Axial Stress Strain Factor of Safety Bending Stress Shear Stress Beam Selection Deflection Evaluation and Redesign.](https://reader035.fdocuments.in/reader035/viewer/2022062219/55182ccc5503469d318b4e89/html5/thumbnails/1.jpg)
Beam Design
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Beam Design
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Beam Design
• Beams are designed to safely support the design loads.
• Beams are primarily designed for bending and shear.
• Beam deflection must be checked.• Beams are sized to minimize material.
Deflection
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Steps in Beam Design
1. Establish the design loads2. Analyze the beam3. Select the preliminary member4. Evaluate the preliminary design5. Redesign (if needed) – Repeat the above
steps as necessary to achieve a safe and efficient design
6. Design and detail the structural component
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Stress
• A measure of the magnitude of the internal forces acting between particles of the member resulting from external forces
• Expressed as the average force per unit area
Force F
StressArea A
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Axial Stress
• Tension and compression
• Axial stress represented by
Where F = applied force A = cross sectional area resisting load
FA
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Axial Stress
Example: Find the tensile stress of a 2 in. x 3 in. tension member subjected to a 45 kip axial load.
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Strain
• The change in size or shape of a material caused by the application of external forces
• Axial strain,
Where = change in length L = original length
LL
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Strain
Example: Calculate the strain if a 16 ft long structural member elongates 1.5 in. when subjected to a tensile load of 67 kips.
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Stress and Strain
• In many materials, stress is directly related to strain up to a certain point.
RiseRun
E
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Stress and Strain
• Elastic behavior – material will return to its original shape when unloaded
• Plastic behavior – material will retain some deformation when unloaded
• Structural members are designed to act elastically during the service life of a building
Yield Point
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Factor of Safety
• The ratio of the maximum safe load to the maximum allowable design load
• Magnitude of the factor of safety varies depending on the loading conditions and type of forces induced
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Allowable Strength Design (ASD)
• Strength is related to stress– Strength indicates internal force– Stress indicates internal force per unit area
• ASD limits the maximum internal force within a structural member
• Maximum safe load = nominal strength– Internal force that causes yielding across the
entire cross section
• Maximum allowable load = allowable strength
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Allowable Strength Design (ASD)
Where = factor of safety
= nominal strength
= internal force due to design loads
= allowable strength
OR
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Where = 1.67 = factor of safety for bending
= nominal bending moment strength
= internal bending moment due to design loads
= allowable bending strength
Allowable Bending Strength
OR
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Nominal Bending Strength
Where = yield stress of steel= plastic section modulus
NOTE: We will assume that every beam and girder is laterally supported along its length so that it will not buckle under loading. If a beam is not laterally supported, buckling must be checked.
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Plastic Section Modulus, Z
• Section property
• Indicates the moment carrying capacity of a member
• Available in tabular form in design manuals
http://www.structural-drafting-net-expert.com/
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• I-shaped members are excellent choices for beams
• Structural steel wide flange
• Designation W
• Example: W12 x 58
• Stronger when bending about the x – x axis, Zx
Plastic Section Modulus, ZFlange
Flange
Web
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Where = 1.5 = factor of safety for shear
= nominal shear strength
= internal shear force due to design loads
= allowable shear strength
Allowable Shear Strength
OR
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Nominal Shear Strength
Where = nominal shear strength
= yield stress of steel
Aw = area of the web
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Beam Deflection
• Deflection limit supporting plaster ceilings– L/240 for Dead + Live Loads– L/360 of Live Load
• Deflection limit supporting non-plaster ceilings– L/180 for Dead + Live Loads– L/240 of Live Load
• WHY?– Ceiling cracks in plaster– Roof ponding (flat roofs)– Visual or psychological reasons– Designer’s judgment
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Beam Selection Process
• Select beam based on bending moment
• Check shear strength
• Check deflection
• Revise beam selection as necessary
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Beam Design Example
Choose the lightest wide flange steel section available to support a live load of 790 plf and a dead load of 300 plf over a simple span of 18 feet. Assume the beam will support a plaster ceiling. Use Fy = 50 ksi.
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Beam Design Example
Max Shear
Max Bending Moment
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Bending Strength
Select beam based on bending.
where
= 1.67
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2
73 722 12
50 000 1 x lbin
, ft lb in.Z
, ft
Bending Strength
Since
W10 x 17 works Z x = 18.7 in.3 > 17.7 in.3
But a W 12 x 16 weighs less with Z x = 20.1 in.3 > 17.7 in.3
3in.xZ 17 7
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Shear Strength
Check shear strength.
where
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Shear Strength
Since and
W12 x 16 works
For a W 12 x 16 d = 11.99 in. t w =0.220 in.
79,134 lb ≥ 14,715 lb
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Check DeflectionDeflection limit supporting plaster ceilings
– L/240 for Dead + Live Loads
– L/360 of Live Load
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Check DeflectionMaximum deflection due to design loads
– Dead + Live Load Deflection
W 12 x 16 will work
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Check DeflectionMaximum deflection due to design loads
– Live Load Deflection
W 12 x 16 will not work
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Evaluation and RedesignCheck Deflection
Try W 12 x 19
Dead + Live Deflection
W 12 x 19 OK
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Evaluation and RedesignCheck Shear and Bending Moment
By inspection, the plastic section modulus and web area for the W12 x 19 are larger than those for the W12 x 16 and are therefore sufficient to safely support the bending moment and shear.
Use a W12 X 19
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Beam Design