Load-Carrying Capacity of a Bolted Joint Given: A ½ in.-13UNC grade 5 steel bolt clamps two steel plates and loaded as shown in Figure 15.11a. Find: The maximum load based on a safety factor of 2. Assumption: The connection will be permanent. Joint stiffness is taken as C = 0.35 (a detailed

Question

Load-Carrying Capacity of a Bolted Joint

Given: A ½ in.-13UNC grade 5 steel bolt clamps two steel plates and loaded as shown in Figure 15.11a.

Find: The maximum load based on a safety factor of 2.

Assumption: The connection will be permanent. Joint stiffness is taken as [latex]C[/latex] = 0.35 (a detailed discussion about this is in Section 15.11).

Accepted Answer

For the ½-13UNC grade 5 steel bolt, we have

[latex]A_{t}[/latex] = 0.1419 in². (by Table 15.1)

[latex]S_{p}[/latex] = 85 ksi (from Table 15.4)

Applying Equation 15.27, the maximum load that the bolt can safely support is then

[latex] n=\frac{S_p A_t-F_i}{C P} [/latex] (15.27)

[latex] P_{\max , b}=\frac{S_p A_t-F_i}{n C}=\frac{(85)(0.1419)-10.86}{2(0.35)}=1.716 kips [/latex]

By Equation 15.28a, the maximum load before separation takes place equals

[latex] P_{ s }=\frac{F_i}{(1-C)} [/latex] (15.28a)

[latex] P_{\max , p}=\frac{F_i}{n(1-C)}=\frac{10.86}{2(1-0.35)}=8.35 kips [/latex]

Comment: Failure owing to separation of art will not take place prior to bolt failure.

Table 15.1 Dimensions of Unified Screw Threads
Course Threads—UNC					Fine Threads—UNF
Size	Major Diameter, [latex]d[/latex] (in.)	Threads per Inch, N = 1/p	Minor Diameter [latex]d_{r}[/latex] (in.)	Tensile Stress Area, [latex]A_{t}[/latex], (in.²)	Threads per Inch, N = l/p	Minor Diameter, [latex]d_{r}[/latex] (in.)	Tensile Stress Area, [latex]A_{t}[/latex] (in.²)
1	0.073	64	0.0538	0.00263	72	0.0560	0.00278
2	0.086	56	0.0641	0.00370	64	0.0668	0.00394
3	0.099	48	0.0734	0.00487	56	0.0771	0.00573
4	0.112	40	0.0813	0.00604	48	0.0864	0.00661
5	0.125	40	0.0943	0.00796	44	0.0971	0.00830
6	0.138	32	0.0997	0.00909	40	0.1073	0.01015
8	0.164	32	0.1257	0.0140	36	0.1299	0.01474
10	0.190	24	0.1389	0.0175	32	0.1517	0.0200
12	0.216	24	0.1649	0.0242	28	0.1722	0.0258
1/4	0.250	20	0.1887	0.0318	28	0.2062	0.0364
3/8	0.375	16	0.2983	0.0775	24	0.3239	0.0878
1/2	0.500	13	0.4056	0.1419	20	0.4387	0.1599
5/8	0.625	11	0.5135	0.226	18	0.5368	0.256
3/4	0.750	10	0.6273	0.334	16	0.6733	0.373
7/8	0.875	9	0.7387	0.462	14	0.7874	0.509
1	1.000	8	0.8466	0.606	12	0.8978	0.663
Source: ANSI/ASME Standards, B1.1–2014, B1.13–2005, New York, American Standards Institute, 2005. Note: The pitch or mean diameter [latex] d_m \approx d-0.65 p [/latex].

Table 15.4 SAE Specifications and Strengths for Steel Bolts
SAE Grade	Size Range Diameter, [latex]d[/latex] (in.)	Proof Strength,[latex]^{a}[/latex] [latex]S_{p}[/latex] (ksi)	Yield Strength,[latex]^{b}[/latex] [latex]S_{y}[/latex] (ksi)	Tensile Strength,[latex]^{b}[/latex] [latex]S_{u}[/latex] (ksi)	Material Carbon Content
1	[latex]\frac{1}{4}-1 \frac{1}{2}[/latex]	33	36	60	Low or medium
2	[latex]\frac{1}{4}-\frac{3}{4}[/latex]	55	57	74	Low or medium
2	[latex]\frac{7}{8}-1 \frac{1}{2}[/latex]	33	36	60	Low or medium
5	[latex]\frac{1}{4}-1[/latex]	85	92	120	Medium, CD
5	[latex]1 \frac{1}{8}-1 \frac{1}{2}[/latex]	74	81	105	Medium, CD
7	[latex]\frac{1}{4}-1 \frac{1}{2}[/latex]	105	115	133	Medium, alloy, Q&T
8	[latex]\frac{1}{4}-1 \frac{1}{2}[/latex]	120	130	150	Medium, alloy, Q&T
Source: Society of Automotive Engineers Standard J429k, 2011. [latex]^{a}[/latex]Corresponds to permanent set not over 0.0001 in. [latex]^{b}[/latex]Offset of 0.2%. Q&T, quenched and tempered.

Question 15.4: Load-Carrying Capacity of a Bolted Joint Given: A ½ in.-13UN...

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