(a)
The adequacy of the W 6 X12 beam for use as purlin using LRFD method.
Answer to Problem 5.5.16P
The beam is adequate to be used for purlin.
Explanation of Solution
Given:
A truss with a roof system supporting a total gravity load of 40 psf of roof surface, half dead load and half snow. Spacing = 10 ft on centers.
Calculation:
Let’s calculate the nominal flexural strength about the X and Y axes.
Determine the strong axis bending strength. As neither the beam design charts nor the Z tables include shapes under W8 compute the flexural strength of W 6 X12. As there is no foot note to indicate otherwise the shape is compact.
We need to determine what controls the lateral torsional buckling.
Computing the values of
Substitute the values from the AISC Manual as
Substitute the values from the AISC Manual as
Now calculate the plastic moment for the section, we have
Where,
Substitute the values from the ASIC manual, we have
Let’s compare the values
Which implies that the strength is governed by inelastic Lateral- Torsional Buckling.
Compute the nominal strength of beam using the equation given as follows:
Substitute the values from the ASIC manual, we have
For the Y − axis, there is no flange buckling since the shape is compact.
Calculate the flexural strength about y- axis as:
Where,
Now, calculating the plastic moment of section about minor principal axis as:
Substitute the values, we have
Calculate the flexural strength about y axis, we have
Checking the upper limit using the following :
Substitute the values, we have
As the inequality is satisfied then the its OK.
Now using the LRFD method.
Following equation must be satisfied in order to know adhere to AISC specifications.
Where,
Now we need to find the values to substitute them
Where,
Where,
Where
As it is been given that half of load is dead load and half is snow load.
Therefore, as per the given conditions
Where,
Following is the diagram from which we can find the value of angles.
Substitute the value for H = 6 ft and
Substitute the values
Substitute,
Find the flexural load about x-axis,
Similarly, for
Where,
Substitute,
Find the flexural load about x-axis,
Now, find the values of
As we have found every value, now we can substitute the values and check the adequacy
The equation is hence satisfied.
Conclusion:
Therefore, the beam is adequate.
(b)
The adequacy of W 6 X12 beam for use as purlin using ASD method.
Answer to Problem 5.5.16P
The beam is adequate to be used for purlin.
Explanation of Solution
Given:
A truss with a roof system supporting a total gravity load of 40 psf of roof surface, half dead load and half snow. Spacing = 10 ft on centers.
Calculation:
Now from Allowable stress design
Where
Now find the value of
Where,
Where,
Where
As it is been given that half of load is dead load and half is snow load.
Therefore, as per the given conditions
Calculate the load on the purlin as follows:
Following is the diagram from which we can find the value of angles.
Where,
Substitute the value for H = 6 ft and
Load on the purlin is as follows:
Substitute the values, we have
Now,
Where, L is the length of the beam and
Where,
Substitute the values, we have
Now find the value of
As we have found every value, now we can substitute the values and check the adequacy
Hence, the equation is satisfied.
Conclusion:
Therefore, the beam is adequate.
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