Problem

A rectangular rosette strain gage (Figure 2.20b) is cemented to the free surface of a mach...

A rectangular rosette strain gage (Figure 2.20b) is cemented to the free surface of a machine part made of class 30, gray cast iron (Table A.1). In a test of the part, the following strains were recorded: ϵa = 0.00080, ϵb = 0.00010, and ϵc = 0.00040. Determine the stress components at the point on the surface with respect to the x–y axis shown.

FIGURE 2.20 Rosette strain gages. (a) Delta rosette. (b) Rectangular rosette.

TABLE A.1: Properties in S.I. Units

Material	Density [103 Kg/m3]	Yieldstress[MPa]	Ultimatestress[MPa]		Poisson’sratio		Young'smodulus[GPa]		Percent elongation at rupture		Thermal coefficient [10−6/°C]
STEEL
Structural, ASTM A36	7.85	250		400		0.29		200		30		11.7
AISI-C 1018, cold drawn	7.85	370		440		0.29		200		15		11.7
AISl-C 1030, normalized	7.85	340		530		0.29		200		30		11.7
AISI-C 1040, normalized	7.85	390		590		0.29		200		28		11.7
AISI-C 1080, normalized	7.85	520		1010		0.29		200		11		11.7
ASSI-3140, normalized	7.85	620		900		0.29		200		19		11.7
AISI-4340, normalized	7.8	860		1310		0.29		200		12		11.7
AISI 301 Stainless, annealed	7.92	280		760		0.27		193		60		17.3
AISI 301 Stainless, half hard	7.92	760		1030		0.27		193		15		17.3
CAST IRON
Gray, Class 30 (tension)	7.21	—		210		0.20		103		nil		12.1
Gray, Class 30 (compression)	7.21	—		510		0.20		103		nil		12.1
Gray, Class 40 (tension)	7.21	—		410		0.20		138		nil		12.1
Gray, Class 40 (compression)	7.21	—		990		0.20		138		nil		12.1
ALUMINUM ALLOYS
1100-H12	2.71	103		110		0.33		70.0		25		23.5
2024 T4	2.77	320		470		0.33		74.5		19		22.5
6061 T6	2.7	275		310		0.33		69.0		12		23.6
6063 T5	2.7	145		185		0.33		69.0		12		23.4
7075 T6	2.77	500		570		0.33		72.0		11		22.5
COPPER ALLOYS
Free-Cutting Copper, soft	8.91	62		220		0.35		117		42		17.6
Free-Cutting Copper, hard	8.91	290		320		0.35		117		12		17.6
Yellow Brass, annealed	8.43	117		340		0.35		105		60		20.0
Yellow Brass, half hard	8.43	340		420		0.35		105		23		20.0
Commercial Bronze, annealed	8.84	90		270		0.35		110		45		18.0
Commercial Bronze, half hard	8.84	280		330		0.35		110		25		18.0
TITANIUM
Alloy Ti–Al–V	4.54	890		930		0.33		114		12		9.5
TIMBER (12% MC)
Coastal Douglas Fir (bending)	0.48	—		85		—		13.4		—		3.1–4.5a
Loblolly Pine (bending)	0.51	—		88		—		12.3		—		3.1–4.5a
White Oak (bending)	0.68	—		105		—		12.3		—		3.1–4.5a
CONCRETE
Medium Strength (compression)	2.32	—		28		0.15		25.0		—		9.9

aParallel to the grain.

Step-by-Step Solution

Request Professional Solution

Request Solution!

We need at least 10 more requests to produce the solution.

0 / 10 have requested this problem solution

The more requests, the faster the answer.

Request! (Login Required)

All students who have requested the solution will be notified once they are available.

Add your Solution

Textbook Solutions and Answers Search

Solutions For Problems in Chapter 3

Free Homework Help App

Download From Google Play

Scan Your Homework
to Get Instant Free Answers

Need Online Homework Help?

Ask a Question

Get Answers For Free
Most questions answered within 3 hours.

Recent Solutions