A steel cantilever beam, of length 2L, has an l-section, see Figure Q3. The cantilever beam is undera uniformly distributed load q = 175 kN/m applied in its vertical plane of symmetry at OA part of thespan. The yield strength of the steel is [a] = 440 MPa; the Young's modulus E = 250 GPa. L=1mand the coordinates of Point H are x= 0 mm, y = -80 mm, z= 0 mm.b)Od)LqALDeflection -Rotation -BXFigure Q320mm10mm H20mmThe von Mises equivalent stresses at point H can be calculated asулa)The factors of safety predicted at point H by the maximum shear stress theory of failure (Trescacriterion)-220mmb180mmc)The factors of safety at point H predicted by the maximum-distortion-energy theory (von Misescriterion) can be calculated asMPaBy use of the virtual work method, determine the rotation and deflection at the end B.mm (Downward deflection is negative)x 10-3 radians (Positive rotation is in the anticlockwise direction)

A steel cantilever beam, of length 2L, has an l-section, see Figure Q3. The cantilever beam is under a uniformly distributed load q = 175 kN/m applied in its vertical plane of symmetry at OA part of the span. The yield strength of the steel is [a] = 440 MPa; the Young's modulus E = 250 GPa. L=1m and the coordinates of Point H are x= 0 mm, y = -80 mm, Z= 0 mm. O b) L q A L B X Figure Q3 20mm 10mm H 20mm The von Mises equivalent stresses at point H can be calculated as -220mm b 180mm a) The factors of safety predicted at point H by the maximum shear stress theory of failure (Tresca criterion) MPa c) The factors of safety at point H predicted by the maximum-distortion-energy theory (von Mises criterion) can be calculated as

A steel cantilever beam, of length 2L, has an l-section, see Figure Q3. The cantilever beam is under a uniformly distributed load q = 175 kN/m applied in its vertical plane of symmetry at OA part of the span. The yield strength of the steel is [a] = 440 MPa; the Young's modulus E = 250 GPa. L=1m and the coordinates of Point H are x= 0 mm, y = -80 mm, Z= 0 mm. O b) L q A L B X Figure Q3 20mm 10mm H 20mm The von Mises equivalent stresses at point H can be calculated as -220mm b 180mm a) The factors of safety predicted at point H by the maximum shear stress theory of failure (Tresca criterion) MPa c) The factors of safety at point H predicted by the maximum-distortion-energy theory (von Mises criterion) can be calculated as

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

A steel cantilever beam, of length 2L, has an l-section, see Figure Q3. The cantilever beam is under
a uniformly distributed load q = 175 kN/m applied in its vertical plane of symmetry at OA part of the
span. The yield strength of the steel is [a] = 440 MPa; the Young's modulus E = 250 GPa. L=1m
and the coordinates of Point H are x= 0 mm, y = -80 mm, z= 0 mm.
b)
O
d)
L
q
A
L
Deflection -
Rotation -
B
X
Figure Q3
20mm
10mm H
20mm
The von Mises equivalent stresses at point H can be calculated as
ул
a)
The factors of safety predicted at point H by the maximum shear stress theory of failure (Tresca
criterion)
-220mm
b
180mm
c)
The factors of safety at point H predicted by the maximum-distortion-energy theory (von Mises
criterion) can be calculated as
MPa
By use of the virtual work method, determine the rotation and deflection at the end B.
mm (Downward deflection is negative)
x 10-3 radians (Positive rotation is in the anticlockwise direction)

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