Solution to Problem 203 Stress-strain Diagram | Strength of Materials Review at MATHalino

Problem 203
The following data were recorded during the tensile test of a 14-mm-diameter mild steel rod. The gage length was 50 mm.

Load (N)	Elongation (mm)	Load (N)	Elongation (mm)
0	0	46 200	1.25
6 310	0.010	52 400	2.50
12 600	0.020	58 500	4.50
18 800	0.030	68 000	7.50
25 100	0.040	59 000	12.5
31 300	0.050	67 800	15.5
37 900	0.060	65 000	20.0
40 100	0.163	65 500	Fracture
41 600	0.433

Plot the stress-strain diagram and determine the following mechanical properties: (a) proportional limits; (b) modulus of elasticity; (c) yield point; (d) ultimate strength; and (e) rupture strength.

Solution 203

Click here to show or hide the solution

Area, A = 0.25π(14²) = 49π mm²
Length, L = 50 mm
Strain = Elongation/Length
Stress = Load/Area

Load (N)	Elongation (mm)	Strain (mm/mm)	Stress (MPa)
0	0	0	0
6 310	0.010	0.0002	40.99
12 600	0.020	0.0004	81.85
18 800	0.030	0.0006	122.13
25 100	0.040	0.0008	163.05
31 300	0.050	0.001	203.33
37 900	0.060	0.0012	246.20
40 100	0.163	0.0033	260.49
41 600	0.433	0.0087	270.24
46 200	1.250	0.025	300.12
52 400	2.500	0.05	340.40
58 500	4.500	0.09	380.02
68 000	7.500	0.15	441.74
59 000	12.500	0.25	383.27
67 800	15.500	0.31	440.44
65 000	20.000	0.4	422.25
61 500	Failure		399.51

From stress-strain diagram:

Proportional Limit = 246.20 MPa
Modulus of Elasticity
E = slope of stress-strain diagram within proportional limi
E = 246.20/0.0012 = 205 166.67 MPa = 205.2 GPa
Yield Point = 270.24 MPa
Ultimate Strength = 441.74 MPa
Rupture Strength = 399.51 MPa

Tags:

stress-strain diagram

modulus of elasticity

Add new comment
168910 reads

More Reviewers

Algebra	Engineering Mechanics
Spherical Trigonometry	Strength of Materials
Plane Trigonometry	Structural Analysis
Plane Geometry	General Engineering
Solid Geometry	Derivation of Formulas
Analytic Geometry	Fluid Mechanics and Hydraulics
Integral Calculus	Geotechnical Engineering
Differential Calculus	Reinforced Concrete Design
Elementary Differential Equations	Surveying and Transportation Engineering
Advance Engineering Mathematics	Timber Design
Engineering Economy