Question 9.4: Perform an adequacy assessment of the statically loaded weld...

(a) From Table 9–3, S_{y} = 50  kpsi, S_{ut} = 62  kpsi. From Table 9–2, second pattern, b = 0.375 in, d = 2 in, so

A = 1.414hd = 1.414(0.375)2 = 1.06  in^{2}
I_{u} = d^{3}/6 = 2^{3}/6 = 1.33  in^{3}
I = 0.707hI_{u} = 0.707(0.375)1.33 = 0.353  in^{4}

Table 9–2    Bending Properties of Fillet Welds*

Unit Second Moment of Area	Location of G	Throat Area	Weld
I_{u} =\frac {d^{3}}{12}	\overline { x}=0 \overline { y}=d/2	A= 0.707hd
I_{u} =\frac {d^{3}}{6}	\overline { x}=b/2 \overline { y}=d/2	A= 1.414hd
I_{u} =\frac {bd^{2}}{2}	\overline { x}=b/2 \overline { y}=d/2	A= 1.414hd
I_{u} =\frac {d^{2}}{12}(6b + d )	\overline{x} =\frac {b^{2}}{2b + d} \overline { y}=d/2	A= 0.707h(2b + d)
I_{u} =\frac {2d^{3}}{3} − 2d^{2}\overline{y} + (b + 2d ) \overline{y}^{2}	\overline { x}=b/2 \overline { y}=\frac {d^{2}}{b+2d}	A= 0.707h(b + 2d)
I_{u} =\frac {d^{2}}{6}(3b + d )	\overline { x}=b/2 \overline { y}=d/2	A= 1.414h(b+ d)
I_{u} =\frac {2d^{3}}{3} − 2d^{2}\overline{y} + (b + 2d ) \overline{y}^{2}	\overline { x}=b/2 \overline { y}=\frac {d^{2}}{b+2d}	A = 0.707h(b+ 2d)
I_{u} =\frac {d^{2}}{6}(3b + d )	\overline { x}=b/2 \overline { y}=d/2	A = 1.414h(b + d)
l_{u }= πr^{3}		A =1.414πhr

*I_{u}, unit second moment of area, is taken about a horizontal axis through G, the centroid of the weld group, h is weld size; the plane of the bending couple is normal to the plane of the paper and parallel to the y-axis; all welds are of the same size.

Table 9–3   Minimum Weld-Metal Properties

*The American Welding Society (AWS) specification code numbering system for electrodes. This system uses an E prefixed to a fouror five-digit numbering system in which the first two or three digits designate the approximate tensile strength. The last digit includes variables in the welding technique, such as current supply. The next-to-last digit indicates the welding position, as, for example, flat, or vertical, or overhead. The complete set of specifications may be obtained from the AWS upon request.

Primary shear:

τ^{′}=\frac {F}{A} =\frac {500(10^{−3})}{1.06} = 0.472  kpsi

Secondary shear:

τ^{″} =\frac {Mr}{I} =\frac {500(10^{−3})(6)(1)}{0.353} = 8.50 kpsi

The shear magnitude τ is the Pythagorean combination

τ = (τ^{′2} + τ^{″2})^{1/2} = (0.4722 + 8.502)^{1/2} = 8.51 kpsi

The factor of safety based on a minimum strength and the distortion- energy criterion is

n =\frac {S_{sy}}{τ} =\frac {0.577(50)}{8.51} = 3.39

Since n ≥ n_{d} , that is, 3.39 ≥ 3.0, the weld metal has satisfactory strength.

(b) From Table A–20, minimum strengths are S_{ut} = 58 kpsi and S_{y} = 32 kpsi.

Table A–20   Deterministic ASTM Minimum Tensile and Yield Strengths for Some Hot-Rolled (HR) and Cold-Drawn (CD) Steels [The strengths listed are estimated ASTM minimum values in the size range 18 to 32 mm ( \frac {3}{4}  to 1\frac {1}{4}in). These strengths are suitable for use with the design factor defined in Sec. 1–10, provided the materials conform to ASTM A6 or A568 requirements or are required in the purchase specifications. Remember that a numbering system is not a specification.] Source: 1986 SAE Handbook, p. 2.15

Then

σ =\frac {M}{I/c} =\frac {M}{bd^{2}/6} =\frac {500(10^{−3})6}{0.375(2^{2})/6} = 12  kpsi
n =\frac {S_{y}}{σ} =\frac {32}{12} = 2.67

Since n < n_{d}, that is, 2.67 < 3.0, the joint is unsatisfactory as to the attachment strength.

(c) From part (a), τ = 8.51 kpsi. For an E6010 electrode Table 9–6 gives the allowable shear stress τ_{all} as 18 kpsi. Since τ < τ_{all}, the weld is satisfactory. Since the code already has a design factor of 0.577(50)/18 = 1.6 included at the equality, the corresponding factor of safety to part (a) is

n = 1.6 \frac {18}{8.51} = 3.38

which is consistent.

Table 9–6    Allowable Steady Loads and Minimum Fillet Weld Sizes

Schedule B: Minimum Fillet Weld Size, h	Schedule A: Allowable Load for Various Sizes of Fillet Welds
Not to exceed the thickness of the thinner part. *Minimum size for bridge application does not go below \frac {3}{16} in. †For minimum fillet weld size, schedule does not go above \frac {3}{16} in fillet weld for every \frac {3}{4} in material.	Strength Level of Weld Metal (EXX)
	60*	110*	100	90*	80	70*	60*
	Allowable shear stress on throat, ksi (1000 psi) of fillet weld or partial penetration groove weld
	36.0	33.0	30.0	27.0	24.0	21.0	18.0	τ =
	llowable Unit Force on Fillet Weld, kip/linear in
	25.45h	23.33h	21.21h	19.09h	16.97h	14.85h	12.73h	† f =
	able Unit Force for Various Sizes of Fillet Welds							Leg Size h, in
	25.45	23.33	21..21	19.09	16.97	14.85	12.73	1
	22.27	20.41	18.57	16.70	14.85	12.99	11.14	7/8
	19.09	17.50	15.92	14.32	12.73	11.14	9.55	3/4
	15.91	14.58	13.27	11.93	10.61	9.28	7.96	5/8
	12.73	11.67	10.61	9.54	8.48	7.42	6.37	1/2
	11.14	10.21	9.28	8.35	7.42	6.50	5.57	7/16
	9.54	8.75	7.95	7.16	6.36	5.57	4.77	3/8
	7.95	7.29	6.63	5.97	5.30	4.64	3.98	5/16
	6.36	5.83	5.30	4.77	4.24	3.71	3.18	1/4
	4.77	4.38	3.98	3.58	3.18	2.78	2.39	3/16
	3.18	2.92	2.65	2.39	2.12	1.86	1.59	1/8
	1.59	1.46	1.33	1.19	1.06	0.930	0.795	1/16

*Fillet welds actually tested by the joint AISC-AWS Task Committee.
†f0.707h τ all.