A large electrical transformer is to be suspended from a roof truss of a building. The total weight of the transformer is 32 000 lb. Design the means of support.

Question

Accepted Answer

Objective

Design the means of supporting the transformer.

Given

The total load is 32 000 lb. The transformer will be suspended below a roof truss inside a building. The load can be considered to be static. It is assumed that it will be protected from the weather and that temperatures are not expected to be severely cold or hot in the vicinity of the transformer.

Basic Design Decisions

Two straight, cylindrical rods will be used to support the transformer, connecting the top of its casing to the bottom chord of the roof truss. The ends of the rod will be threaded to allow them to be secured by nuts or by threading them into tapped holes. This design example will be concerned only with the rods. It is assumed that appropriate attachment points are available to allow the two rods to share the load equally during service. However, it is possible that only one rod will carry the entire load at some point during installation. Therefore, each rod will be designed to carry the full 32 000 lb.

We will use steel for the rods, and because neither weight nor physical size is critical in this application, a plain, medium-carbon steel will be used. We specify AISI 1040 cold-drawn steel. From Appendix 3. we find that it has a yield strength of 71 ksi and moderately high ductility as represented by its 12% elongation. The rods should be protected from corrosion by appropriate coatings.

The objective of the design analysis that follows is to determine the size of the rod.

Analysis

The rods are to be subjected to direct normal tensile stress. Assuming that the threads at the ends of the rods are cut or rolled into the nominal diameter of the rods, the critical place for stress analysis is in the threaded portion.Use the direct tensile stress formula. Equation (3_1): σ = F/A. We will first compute the design stress and then compute the required cross-sectional area to maintain the stress in service below that value. Finally, a standard thread will be specified from the data in Chapter 18 on fasteners.

Case CI from Section 5_9 applies for computing the design stress because the rod is made from a ductile steel and it carries a static load. The design stress is

[latex]\sigma _{d}=s_{y}/N [/latex]

We specify a design factor of N = 3, because it is typical for general machine design and because there is some uncertainty about the actual installation procedures that may be used (see Section 5_7). Then

[latex]\sigma_{d}=s_{y} / N=(71000 \mathrm{psi}) / 3=23667 \mathrm{psi}[/latex]

Results

In the basic tensile stress equation, σ = F/A. we know F. and we will let [latex]\sigma =\sigma _{d}[/latex]. Then the required cross-sectional area is

[latex]A=F / \sigma_{d}=(32000 \mathrm{lb}) /\left(23667 \mathrm{lb} / \mathrm{in}^{2}\right)=1.35 \mathrm{in}^{2}[/latex]

A standard size thread will now be specified from the data in Chapter 18 on fasteners. You should be familiar with such data from earlier courses. Table A2_2(b)

		Coarse threads: UNC		Fine threads: UNF
Size	Basic major diameter, D (in)	Threads per inch, n	Tensile stress area ([latex]in^{2}[/latex])	Threads per inch, n	Tensile stress area ([latex]in^{2}[/latex])
1/4	0.2500	20	0.0318	28	0.0364
5/16	0.3125	18	0.0524	24	0.0580
3/8	0.3750	16	0.0775	24	0.0878
7/16	0.4375	14	0.1063	20	0.1187
1/2	0.5000	13	0.1419	20	0.1599
9/16	0.5625	12	0.182	18	0.203
5/8	0.6250	11	0.226	18	0.256
3/4	0.7500	10	0.334	16	0.373
7/8	0.8750	9	0.462	14	0.509
1	1.000	8	0.606	12	0.663
[latex]1^{\frac{1}{8} } [/latex]	1.125	7	0.763	12	0.856
[latex]1^{\frac{1}{4} } [/latex]	1.250	7	0.969	12	1.073
[latex]1^{\frac{3}{8} } [/latex]	1.375	6	1.155	12	1.315
[latex]1^{\frac{1}{2} } [/latex]	1.500	6	1.405	12	1.581
[latex]1^{\frac{3}{4} } [/latex]	1.750	5	1.90
2	2.000	44	2.50

lists the tensile stress area for American Standard threads. [latex]A\mid \frac{1}{2}-6 [/latex] UNC thread ([latex]\mid\frac{1}{2}[/latex]-in-diameter rod with 6 threads per in) has a tensile stress area of 1.405 [latex]in^{2} [/latex] which should be satisfactory for this application.

Comments

The final design specifies a [latex]\mid\frac{1}{2}[/latex]-in-diameter rod made from AISI 1040 cold-drawn steel with [latex]\mid\frac{1}{2}[/latex]-6 UNC threads machined on each end to allow the attachment of the rods to the transformer and to the truss.

Question 5.DE.1: A large electrical transformer is to be suspended from a roo...

Related Answered Questions