Problem #3: A wide-flange beam, constructed with A572 steel, is cooled to -30°C and is subjected to dynamic loading. There is an edge crack in the top flange of 16 mm, as demonstrated in the figure below. 7.5 mm crack a y 13.1 mm -X 203 mm Cross-Section 303 mm a = 16 mm 203 mm- Sg Top View of Flange 13.1 mm Determine the bending moment about the x-axis that will cause brittle fracture of the beam. Note that negative bending causes the top flange to be subjected to tensile stresses.

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Chapter2: Loads On Structures
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Problem #3: A wide-flange beam, constructed with A572 steel, is cooled to -30°C and is subjected to dynamic
loading. There is an edge crack in the top flange of 16 mm, as demonstrated in the figure below.
Hints:
4
●
7.5 mm
crack
a
y
13.1 mm
X
203 mm
Cross-Section
303 mm
a = 16 mm
ㅏ
↑
203 mm-
Sg
Top View of Flange
Determine the bending moment about the x-axis that will cause brittle fracture of the beam. Note that negative
bending causes the top flange to be subjected to tensile stresses.
13.1 mm
As illustrated in the figure above, treat the top flange as an edge-cracked tension member. Use the
simplified expression for computing K, but still verify that it applies.
The average stress in the top flange can be determined by an My/I calculation, as opposed to a P/A
calculation from previous problems. Compute y based on the mid-depth of the top flange.
Ignore the "fillets" (i.e., the rounded portions of the I-section) when calculating the moment of inertia, I.
Transcribed Image Text:Problem #3: A wide-flange beam, constructed with A572 steel, is cooled to -30°C and is subjected to dynamic loading. There is an edge crack in the top flange of 16 mm, as demonstrated in the figure below. Hints: 4 ● 7.5 mm crack a y 13.1 mm X 203 mm Cross-Section 303 mm a = 16 mm ㅏ ↑ 203 mm- Sg Top View of Flange Determine the bending moment about the x-axis that will cause brittle fracture of the beam. Note that negative bending causes the top flange to be subjected to tensile stresses. 13.1 mm As illustrated in the figure above, treat the top flange as an edge-cracked tension member. Use the simplified expression for computing K, but still verify that it applies. The average stress in the top flange can be determined by an My/I calculation, as opposed to a P/A calculation from previous problems. Compute y based on the mid-depth of the top flange. Ignore the "fillets" (i.e., the rounded portions of the I-section) when calculating the moment of inertia, I.
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