Problem #2: A plate constructed of ASTM A470-8 steel is loaded in tension (P=85 kN) when at room temperature. The plate has a center crack. The pertinent dimensions of the plate are provided herein: S AISI 1144 ASTM A470-8 (Cr-Mo-V) ASTM A517-F AISI 4130 For reference, the table below can be used to estimate the fracture toughness and yield strength of the material. Toughness, Kic at Room Temperature Steel Material Hints: (MPa√m) 66 60 187 110 ● h ● b Кс K₁ Part B: Repeat Part A for a crack length is 14 mm (i.e., a = 14 mm). FOS = Yield Strength (MPa) Part A: Determine the safety factors against brittle fracture and against full cross-sectional yielding if the crack length is 3 mm (i.e., a = 3 mm). Use the simplified expression for computing K, but still verify that it applies. h = 35 mm 1 = 5 mm FOS= Py P 540 620 760 1090 Ultimate Strength (MPa) Part C: Provide a brief discussion on the following: (i) which limit state (brittle fracture or yielding) governed each case? (ii) how did the increased crack length influence the FOS for brittle fracture and for yielding? 840 780 830 1150 Neglect thickness effects when computed Kc. Simply use Kic. The plastic yielding strength (P) can be estimated as the material yield strength (o,) multiplied by the net area at the crack location (Anet) (i.e., subtract out the crack length from the total plate width).
Problem #2: A plate constructed of ASTM A470-8 steel is loaded in tension (P=85 kN) when at room temperature. The plate has a center crack. The pertinent dimensions of the plate are provided herein: S AISI 1144 ASTM A470-8 (Cr-Mo-V) ASTM A517-F AISI 4130 For reference, the table below can be used to estimate the fracture toughness and yield strength of the material. Toughness, Kic at Room Temperature Steel Material Hints: (MPa√m) 66 60 187 110 ● h ● b Кс K₁ Part B: Repeat Part A for a crack length is 14 mm (i.e., a = 14 mm). FOS = Yield Strength (MPa) Part A: Determine the safety factors against brittle fracture and against full cross-sectional yielding if the crack length is 3 mm (i.e., a = 3 mm). Use the simplified expression for computing K, but still verify that it applies. h = 35 mm 1 = 5 mm FOS= Py P 540 620 760 1090 Ultimate Strength (MPa) Part C: Provide a brief discussion on the following: (i) which limit state (brittle fracture or yielding) governed each case? (ii) how did the increased crack length influence the FOS for brittle fracture and for yielding? 840 780 830 1150 Neglect thickness effects when computed Kc. Simply use Kic. The plastic yielding strength (P) can be estimated as the material yield strength (o,) multiplied by the net area at the crack location (Anet) (i.e., subtract out the crack length from the total plate width).
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Problem #2: A plate constructed of ASTM A470-8 steel is loaded in tension (P=85 kN) when at room temperature.
The plate has a center crack. The pertinent dimensions of the plate are provided herein:
S
++
Steel Material
AISI 1144
ASTM A470-8 (Cr-Mo-V)
ASTM A517-F
AISI 4130
a
T
Hints:
T
For reference, the table below can be used to estimate the fracture toughness and yield strength of the material.
Toughness, Kic at
Room Temperature
(MPa√m)
66
60
187
110
h
b-
t
FOS=
Кс
K₁
Part B: Repeat Part A for a crack length is 14 mm (i.e., a = 14 mm).
Yield Strength (MPa)
b = 35 mm
1 = 5 mm
Part A: Determine the safety factors against brittle fracture and against full cross-sectional yielding if the crack
length is 3 mm (i.e., a = 3 mm). Use the simplified expression for computing K, but still verify that it applies.
FOS=
Py
P
540
620
760
1090
Ultimate Strength
(MPa)
840
780
830
1150
Part C: Provide a brief discussion on the following: (i) which limit state (brittle fracture or yielding) governed each
case? (ii) how did the increased crack length influence the FOS for brittle fracture and for yielding?
Neglect thickness effects when computed Kc. Simply use Kic.
The plastic yielding strength (P₂) can be estimated as the material yield strength (ay) multiplied by the net
area at the crack location (Anet) (i.e., subtract out the crack length from the total plate width).
Expert Solution
Step 1
Given:
a = 3 mm
b = 35 mm
t = 5 mm
P = 85 kN
ASTM A470-8 properties:
Kc = KIc = 60 MPa
Yield strength, fy = 620 MPa
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