Question 3.2: A tensile member for a roof truss for a building is to carry...
A tensile member for a roof truss for a building is to carry a static axial tensile load of 88 kN. It has been proposed that a standard, equal-leg structural steel angle be used for this application using ASTM A36 structural steel. Use the AISC code. Specify a suitable angle from Appendix A–5(c).
Objective Specify a standard equal-leg steel angle.
Given F = 88 000 N static load.
Material: ASTM A36; s_{y} = 248 MPa; s_{u} = 400 MPa
(Data from Appendix A–12)
| A–12 Properties of structural steels .^{a} | |||||
| Ultimate strength, s_{u}^{a} | Yield strength, s_{y}^{a} | ||||
| Material ASTM No. and products | ksi | MPa | ksi | MPa | Percent elongation in 2 in. |
| A36—carbon steel; available in shapes,plates, and bars | 58 | 400 | 36 | 248 | 21 |
| A 53—Grade B pipe | 60 | 414 | 35 | 240 | 23 |
| A242—HSLA, corrosion resistant; available in shapes, plates, and bars | |||||
| ≤ \frac{3}{4} in. thick | 70 | 483 | 50 | 345 | 21 |
| 1 \frac{1}{2} in. thick | 67 | 462 | 46 | 317 | 21 |
| 1 \frac{1}{2} to 4 in. thick | 63 | 434 | 42 | 290 | 21 |
| A500—Cold-formed structural tubing | |||||
| Round, Grade B | 58 | 400 | 42 | 290 | 23 |
| Round, Grade C | 62 | 427 | 46 | 317 | 21 |
| Round, Grade B | 58 | 400 | 46 | 317 | 23 |
| Round, Grade C | 62 | 427 | 50 | 345 | 21 |
| A501—Hot-formed structural tubing, round or shaped | 58 | 400 | 36 | 248 | 23 |
| A514—Quenched and tempered alloy steel; available in plate only | |||||
| ≤ 2 \frac{1}{2} in. thick | 110 | 758 | 100 | 680 | 18 |
| 2 \frac{1}{2} to 6 in. thick | 100 | 690 | 90 | 620 | 16 |
| A572—HSLA columbium–vanadium steel; available in shapes, plates, and bars | |||||
| Grade 42 | 60 | 414 | 42 | 290 | 24 |
| Grade 50 | 65 | 448 | 50 | 345 | 21 |
| Grade 60 | 75 | 517 | 60 | 414 | 18 |
| Grade 65 | 80 | 552 | 65 | 448 | 17 |
| A913—HSLA, grade 65; available in shapes only | 80 | 552 | 65 | 448 | 17 |
| A992—HSLA; available in W-shapes only | 65 | 448 | 50 | 345 | 21 |
Analysis Use Case C from Section 3–5.
Case C To Determine the Shape and Dimensions of the Component
Given a. The magnitude and type of loading on the component of interest
b. The material, including its condition, from which the component is to be made
Objective The shape and dimensions of critical geometry of the component
Method 1. Determine the yield strength, ultimate strength, and percent elongation for the selected material. Decide if the material is ductile (percent elongation > 5%) or brittle (percent elongation < 5%).
2. Specify an appropriate design factor considering the type of loading, the type of material, the conditions listed in the preceding section, and recommended guide- lines. For direct normal stresses, use Table 3–2.
3. Compute the design stress from Equation (3-2) or (3-3)
\sigma_{d} = s_{y} /N based on yield strength
\sigma_{d} = s_{u} /N based on ultimate tensile strength
4. Write the equation for the expected maximum stress in the component. For direct normal stresses,
\sigma_{max} = F/A
5. Set \sigma_{max} = \sigma_{d} and solve for the required cross-sectional area.
\sigma_{max} = \sigma_{d} = F/A
Required A=F/ \sigma_{d}
6. Determine the minimum required dimensions of the cross-sectional area to achieve the necessary total area. This is dependent on the shape you choose to make the component. It may be a solid circular, square, or rectangular, a hollow tube, a standard structural shape such as an angle, or some special shape of your own design.
7. Specify convenient dimensions from the list of preferred basic sizes listed in Appendix A–2.
| TABLE 3–2 Design stress guidelines: Direct normal stresses. | ||
| Manner of loading | Ductile material | Brittle material |
| Static | \sigma_{d} = s_{y} /2 | \sigma_{d} = s_{u} /6 |
| Repeated | \sigma_{d} = s_{y} /8 | \sigma_{d} = s_{u} /10 |
| Impact or shock | \sigma_{d} = s_{y} /12 | \sigma_{d} = s_{u} /15 |
| A–2 Preferred basic sizes. | ||||||||
| Fractional (in.) | Decimal (in.) | SI metric (mm) | ||||||
| \frac{1}{64} | 0.015 625 | 5 | 5.000 | 0.010 | 2.00 | 8.50 | 1.0 | 40 |
| \frac{1}{32} | 0.031 25 | 5 \frac{1}{4} | 5.250 | 0.012 | 2.20 | 9.00 | 1.1 | 45 |
| \frac{1}{16} | 0.0625 | 5 \frac{1}{2} | 5.500 | 0.016 | 2.40 | 9.50 | 1.2 | 50 |
| \frac{3}{32} | 0.093 75 | 5 \frac{3}{4} | 5.750 | 0.020 | 2.60 | 10.00 | 1.4 | 55 |
| \frac{1}{8} | 0.1250 | 6 | 6.000 | 0.025 | 2.80 | 10.50 | 1.6 | 60 |
| \frac{5}{32} | 0.156 25 | 6 \frac{1}{2} | 6.500 | 0.032 | 3.00 | 11.00 | 1.8 | 70 |
| \frac{3}{16} | 0.1875 | 7 | 7.000 | 0.040 | 3.20 | 11.50 | 2.0 | 80 |
| \frac{1}{4} | 0.2500 | 7 \frac{1}{2} | 7.500 | 0.05 | 3.40 | 12.00 | 2.2 | 90 |
| \frac{5}{16} | 0.3125 | 8 | 8.000 | 0.06 | 3.60 | 12.50 | 2.5 | 100 |
| \frac{3}{8} | 0.3750 | 8 \frac{1}{2} | 8.500 | 0.08 | 3.80 | 13.00 | 2.8 | 110 |
| \frac{7}{16} | 0.4375 | 9 | 9.000 | 0.10 | 4.00 | 13.50 | 3.0 | 120 |
| \frac{1}{2} | 0.5000 | 9 \frac{1}{2} | 9.500 | 0.12 | 4.20 | 14.00 | 3.5 | 140 |
| \frac{9}{16} | 0.5625 | 10 | 10.000 | 0.16 | 4.40 | 14.50 | 4.0 | 160 |
| \frac{5}{8} | 0.6250 | 10 \frac{1}{2} | 10.500 | 0.20 | 4.60 | 15,00 | 4.5 | 180 |
| \frac{11}{16} | 0.6875 | 11 | 11.000 | 0.24 | 4.80 | 15.50 | 5.0 | 200 |
| \frac{3}{4} | 0.7500 | 11 \frac{1}{2} | 11.500 | 0.30 | 5.00 | 16.00 | 5.5 | 220 |
| \frac{7}{8} | 0.8750 | 12 | 12.000 | 0.40 | 5.20 | 16.50 | 6 | 250 |
| 1 | 1.000 | 12 \frac{1}{2} | 12.500 | 0.50 | 5.40 | 17.00 | 7 | 280 |
| 1 \frac{1}{4} | 1.250 | 13 | 13.000 | 0.60 | 5.60 | 17.50 | 8 | 300 |
| 1 \frac{1}{2} | 1.500 | 13 \frac{1}{2} | 13.500 | 0.80 | 5.80 | 18.00 | 9 | 350 |
| 1 \frac{3}{4} | 1.750 | 14 | 14.000 | 1.00 | 6.00 | 18.50 | 10 | 400 |
| 2 | 2.000 | 14 \frac{1}{2} | 14.500 | 1.20 | 6.50 | 19.00 | 11 | 450 |
| 2 \frac{1}{4} | 2.250 | 15 | 15.000 | 1.40 | 7.00 | 19.50 | 12 | 500 |
| 2 \frac{1}{2} | 2.500 | 15 \frac{1}{2} | 15.500 | 1.60 | 7.50 | 20.00 | 14 | 550 |
| 2 \frac{3}{4} | 2.750 | 16 | 16.000 | 1.80 | 8.00 | 16 | 600 | |
| 3 | 3.000 | 16 \frac{1}{2} | 16.500 | 18 | 700 | |||
| 3 \frac{1}{4} | 3.250 | 17 | 17.000 | 20 | 800 | |||
| 3 \frac{1}{2} | 3.500 | 17 \frac{1}{2} | 17.500 | 22 | 900 | |||
| 3 \frac{3}{4} | 3.750 | 18 | 18.000 | 25 | 1000 | |||
| 4 | 4.000 | 18 \frac{1}{2} | 18.500 | 28 | ||||
| 4 \frac{1}{4} | 4.250 | 19 | 19.000 | 30 | ||||
| 4 \frac{1}{2} | 4.500 | 19 \frac{1}{2} | 19.500 | 35 | ||||
| 4 \frac{3}{4} | 4.750 | 20 | 20.000 | |||||
Let \sigma_= \sigma_{d} = 0.60s_{y} or \sigma_{d} = 0.50s_{u} (Table 3-3)
| TABLE 3–3 Design stress from selected codes: Direct normal stresses—Static loads on building-like structures. | |
| Structural steel (AISC): ASD | |
| \sigma_{d} = s_{y} / 1.67 =0.60s_{y} or \sigma_{d}=s_{u}/2.00 = 0.50s_{u} | |
| whichever is lower | |
| Aluminum (AA): | |
| \sigma_{d} = s_{y} / 1.67 =0.61s_{y} or \sigma_{d}=s_{u}/1.95 = 0.51s_{u} | |
| whichever is lower | |
Stress analysis: \sigma F/A; then required area = A = F/ \sigma_{d}
Results \sigma_{d} = 0.60s_{y} = 0.60(248 MPa) = 148.8 MPa
or \sigma_{d} = 0.50s_{u} = 0.50(400 MPa) = 200 MPa
Use lower value; \sigma_{d} = 148.8 MPa.
Required area: A = F/ \sigma_{d} = (88 000 N)/(148.8 N/mm²) = 591 mm²
This is the minimum allowable area.
pecify: L 60×60×6 steel angle (Appendix A–5(c); lightest equal-leg section).
A = 684 mm²; weight = 51.533 N/m.