Question 7.6: The roof of an industrial building is to be supported by wid...

Objective    Specify a suitable wide-flange beam.

Given          Loading pattern in Figure 7–19; design stress from AISC specifications for ASTM A36 structural steel

Analysis       Design procedure A from this section will be used.

Results        Step 1. We must first determine the load on each beam of the roof structure.

Dividing the load evenly among adjacent beams would result in each beam carrying a 1.5 m wide portion of the roof load. In addition to the 8 kN/m² live load, the weight of

the concrete slab offers a sizeable load. In Section 2–10, we find that the concrete weighs 23.6 kN/m³. Then, each square meter of the roof, 100 mm thick (0.10 m), would have a volume of

V = (1.0 m)(1.0 m)(0.10 m) = 0.10 m³

The weight of each square meter would then be

W = V(23.6 kN/m³)=(0.10 m³)(2.36 kN/m³) = 2.36 kN

This is called the “dead load.”  Then, adding the live load, the total loading due to the roof is 10.36 kN/m². Now, notice that each meter of length of the beam carries 1.5 m² of the roof. Therefore, the load on the beam is a uniformly distributed load of 15 540 N/m. Figure 7–19 shows the loaded beam and the shearing force and bending moment diagrams. The maximum bending moment is 124 320 N m at the middle of the length of the beam.

Steps 2 and 3. Table 7–2 calls for the design stress to be

σ_{d} = 0.66s_{y}

From Appendix A–12, the yield strength of ASTM A36 structural steel is 248 MPa. Then,

^{a} Minimum values; may range higher.
HSLA, an abbreviation for high-strength, low-alloy steel.
The American Institute of Steel Construction specifies E = 29 × 10^6 psi (200 GPa) for structural steel.

σ_{d} = 0.66s_{y} = 0.66(248 MPa) = 164 MPa

Step 4. In order to select an IPE shape beam, the required minimum section modulus must be calculated.

σ_{d} = \frac{M}{S_{min}}

S_{min} = \frac{M}{σ_{d}} = \frac{124  320  N·m \left\lgroup \frac{1000  mm}{1  m} \right\rgroup }{164  N/mm²} = 7.58 \times 10^{5}  mm^{3}

Step 5. This step does not apply in this problem.

Step 6. A beam must be found from Appendix A–7(e), which has a value of S greater than 7.58 \times 10^{5}  mm^{3} . The lightest IPE shape is:

IPE 360×170 : S = 9.036 \times 10^{5}  mm^{3}

Comment            In the final design of the structure, lateral bracing would be required as defined in Reference 5. Also, deflection of the beam should be checked using the methods described in Chapter 9.