Question

Answer 1

The maximum permissible load on the beam is dependent on the nominal strength of the section.

Therefore, compute the nominal strength which is again dependent on the relationship between the unbraced length , and .

From the (plastic modulus) table of the Manual:

The unbraced length of the beam is .

Now, compare the values of,  and:

Substitute for, for and for:

The relation obtained is:

From the properties and dimensions table, as there is no footnote for to indicate non compact section, the section is compact.

Therefore the strength is governed by inelastic Lateral- Torsional Buckling.

Compute the nominal strength of beam using the equation given below:

Here the elastic section modulus about the major principal axis is , the yield strength of steel is , the plastic moment is and the nominal strength of beam is and the factor taken to account for non-uniform bending within the unbraced length is .

To calculate the value of , first compute the number of lateral supports provided by:

Here, the length of the beam is L.

Substitute for L and for:

So, the lateral supports are provided at the quarter points.

From Table 3-1 in Part 3 of the Manual:

Compute the plastic moment for the section as:

Here the plastic section modulus about major principal axis is and the yield strength is.

Substitute for and for for (from part 1 of the Manual):

Compute the nominal strength of beam using the equation given below:

Substitute 1.06 for , for (from the dimensions and properties table in part 1 of the Manual),  for , for , for , for and for :

Compute the maximum service live load as follows:

(a)

Using LRFD:

Compute the design strength of the section as follows:

Here the design strength of beam is .

Substitute 0.9 for and for :

The maximum bending moment for a uniform load is at the centre and is given by:

Here the total uniformly distributed load on the beam is .

Compute as:

...... (1)

Here, the uniformly distributed dead load is and the uniformly distributed live load is .

There is no dead load on the beam apart from the self weight of the beam.

From the dimensions and properties table of part 1 of the Manual:

Find the maximum permissible service live load by equating the design flexural strength and maximum bending moment:

From equation (1), use :

Substitute for , 48 ft for L and for:

The maximum permissible service load is

(b)

Using ASD method:

Compute the design strength of the section as follows:

Here the design strength of beam is .

Substitute 1.67 for and for :

The maximum bending moment for a uniform load is at the centre and is given by:

Here the total uniformly distributed load on the beam is .

Compute as:

...... (2)

Here, the uniformly distributed dead load is and the uniformly distributed live load is .

There is no dead load on the beam apart from the self weight of the beam.

From the dimensions and properties table of part 1 of the Manual:

Find the maximum permissible service live load by equating the design flexural strength and maximum bending moment:

From equation (2), use :

Substitute for , for L and for :

The maximum permissible service load is