Our firm has been selected to design a new manufacturing building in an industrial complex. Because of the sensitivity of the equipment that will be mounted on the roof, we anticipate using a rigid diaphragm. The arrangement of the manufacturing process has dictated the layout of the gravity

Question

Our firm has been selected to design a new manufacturing building in an industrial complex. Because of the sensitivity of the equipment that will be mounted on the roof, we anticipate using a rigid diaphragm. The arrangement of the manufacturing process has dictated the layout of the gravity system and the placement of the diagonal braces for lateral resistance.

Accepted Answer

Using the Directional Procedure for determining the effects of wind on the structure, we have calculated the shear generated in each lateral load-resisting element for case 2, considering wind from the north (Example 11.1). This wind direction causes the largest forces in the north-south—oriented lateral elements.

Client requirements have determined the direction of each diagonal brace.

The shear capacity of the diaphragm is 4.75 kN/m. Our team leader wants us to determine whether the diaphragm is sufficiently strong to transfer the shear just along the braced frame for each column line. If any are not strong enough, we are to determine the fewest possible collector beam segments. For any collectors, we are to label the connection force on a plan view of the framing.

Shear along column line 2:

[latex]l_{ ext {min }}^{ ext {Line } 2} = \frac{51.5 \mathrm{kN}}{4.75 \mathrm{kN} / \mathrm{m}} = 10.8 \mathrm{~m}[/latex]

[latex]10.8 \mathrm{~m} > 6 \mathrm{~m} herefore ext { Need collector beams }[/latex]

[latex]l_{\mathrm{A} 2-\mathrm{D} 2} = 6 \mathrm{~m} + 4 \mathrm{~m} + 5 \mathrm{~m} = 15 \mathrm{~m}[/latex]

[latex]15 \mathrm{~m} > 10.8 \mathrm{~m} herefore ext { Collector beams B2-C2 and C2-D2 }[/latex]

[latex]v_{\mathrm{A} 2-\mathrm{D} 2} = \frac{51.5 \mathrm{kN}}{15 \mathrm{~m}} = 3.43 \mathrm{kN} / \mathrm{m}[/latex]

The shear starts gathering at D2.

[latex]F_{\mathrm{C} 2} = 3.43 \mathrm{kN} / \mathrm{m}(5 \mathrm{~m}) = 17.2 \mathrm{kN}[/latex]

[latex]F_{\mathrm{B} 2} = 3.43 \mathrm{kN} / \mathrm{m}(5 \mathrm{~m} + 4 \mathrm{~m}) = 30.9 \mathrm{kN}[/latex]

Since the diagonal attaches at A2, the shear continues to gather.

[latex]F_{\mathrm{A} 2} = 3.43 \mathrm{kN} / \mathrm{m}(5 \mathrm{~m} + 4 \mathrm{~m} + 6 \mathrm{~m}) = 51.4 \mathrm{kN}[/latex]

Shear along column line 5:

[latex]l_{\min }^{ ext {Line } 5} = \frac{41.3 \mathrm{kN}}{4.75 \mathrm{kN} / \mathrm{m}} = 8.7 \mathrm{~m}[/latex]

[latex]8.7 \mathrm{~m} > 5 \mathrm{~m} herefore ext { Need collector beams }[/latex]

[latex]l_{\mathrm{B} 5-\mathrm{D} 5} = 5 \mathrm{~m} + 4 \mathrm{~m} = 9 \mathrm{~m}[/latex]

[latex]9 \mathrm{~m} > 8.7 \mathrm{~m} herefore ext { Collector beam B5-C5 }[/latex]

[latex]v_{\mathrm{B} 5-\mathrm{D} 5} = \frac{41.3 \mathrm{kN}}{9 \mathrm{~m}} = 4.59 \mathrm{kN} / \mathrm{m}[/latex]

Since the diagonal attaches at C5, the shear gathers toward this point.

[latex]F_{\mathrm{C} 5-\mathrm{D} 5} = 4.59 \mathrm{kN} / \mathrm{m}(5 \mathrm{~m}) = 23.0 \mathrm{kN}[/latex]

[latex]F_{\mathrm{C} 5-\mathrm{B} 5} = 4.59 \mathrm{kN} / \mathrm{m}(4 \mathrm{~m}) = 18.4 \mathrm{kN}[/latex]

Shear along column line 10:

[latex]l_{\min }^{ ext {Line } 10} = \frac{14.3 \mathrm{kN}}{4.75 \mathrm{kN} / \mathrm{m}} = 3.0 \mathrm{~m}[/latex]

[latex]v_{\mathrm{B} 10-\mathrm{C} 10} = \frac{14.3 \mathrm{kN}}{4 \mathrm{~m}} = 3.58 \mathrm{kN} / \mathrm{m}[/latex]

The shear gathers toward the diagonal at C10.

[latex]F_{\mathrm{C} 10} = 3.58 \mathrm{kN} / \mathrm{m}(4 \mathrm{~m}) = 14.3 \mathrm{kN}[/latex]

Summary:

Question 11.4: Our firm has been selected to design a new manufacturing bui...

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