Concept explainers
(a)
Maximum permissible load using LFRD method.
Answer to Problem 5.5.1P
The maximum permissible load from LFRD method is
Explanation of Solution
Given information:
A W 10X 77 has continuous lateral support. The load P is a service live load and
Following is the given beam:
Calculation:
We have following properties for W 10X 77 from ASIC manual
DesignationImperial (in x lb/ft) | Depth h (in) | Width w (in) | Web Thickness tw (in) | Flange Thickness tf (in) | Sectional Area (in2) | Weight (lbf/ft) | Static Parameters | ||||
Moment of Inertia | Elastic Section Modulus | ||||||||||
Ix (in4) | Iy (in4) | Sx (in3) | Sy (in3) | ||||||||
W 10 x 77 | 10.60 | 10.190 | 0.530 | 0.870 | 22.6 | 77 | 455 | 154 | 85.9 | 30.1 |
Let’s check for the compactness of the given W-shape beam using part
For Flange:
Where,
If the above condition satisfies, then the flange is non compact for flexure
Therefore, the web is compact.
Calculate the nominal flexural strength using the formula
Where,
Manual.
Now, calculate the maximum bending moment due to dead load, we have
Maximum bending moment for a simply supported beam carrying a dead UDL
Where,
Substitute,
Calculate the maximum bending moment for a simply supported beam carrying a concentrated
live load of the beam:
Where, P is the concentrated load and L is the length of the beam is.
Now, using Load Resistance and Factored design method:
Calculate the maximum permissible load P.
Substitute
Calculate P, by equating the maximum bending moment with the flexural strength of the beam;
Where,
Substitute
Conclusion:
Therefore, the maximum permissible load from LFRD method is
(b)
Maximum permissible load using ASD method.
Answer to Problem 5.5.1P
The maximum permissible load from ASD method is
Explanation of Solution
Given information:
A W 10X 77 has continuous lateral support. The load P is a service live load and
Calculation:
We have following properties for W 10X 77 from ASIC manual
DesignationImperial (in x lb/ft) | Depthh (in) | Widthw (in) | Web Thicknesstw (in) | Flange Thicknesstf (in) | Sectional Area (in2) | Weight (lbf/ft) | Static Parameters | ||||
Moment of Inertia | Elastic Section Modulus | ||||||||||
Ix (in4) | Iy (in4) | Sx (in3) | Sy (in3) | ||||||||
W 10 x 77 | 10.60 | 10.190 | 0.530 | 0.870 | 22.6 | 77 | 455 | 154 | 85.9 | 30.1 |
Let’s check for the compactness of the given W-shape beam using part
For Flange:
Where,
If the above condition satisfies, then the flange is non compact for flexure
Therefore, the web is compact.
Calculate the nominal flexural strength using the formula
Now, calculate the maximum bending moment due to dead load, we have
Maximum bending moment for a simply supported beam carrying a dead UDL
Where,
Substitute,
Calculate the maximum bending moment for a simply supported beam carrying a concentrated
live load of the beam:
Where, P is the concentrated load and L is the length of the beam is.
Calculate the uniformly distributed load on the beam by equating
Allowable stress design method:
Substitute
Calculate P, by equating the maximum bending moment with the flexural strength of the beam:
Substitute,
Conclusion:
Therefore, the maximum permissible load from ASD method is
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Chapter 5 Solutions
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