A 3m-long, thin-walled section (thickness t = 4 mm, for all elements) is used as a cantilever to support a point load P=2 kN. The point load P acts through the centroid of the cross-section (point c). The section's centreline dimensions are shown, and the moment of inertia about the x-axis is Ixx = 1.94 x 106 mm*. 3a) Determine the horizontal location of the centroid (i.e. calculate b) 3b) Determine the horizontal location of the shear centre (point o) (i.e. calculate d) 3c) Determine the values of the shear force (V), bending moment (M), and torque (7) at the fixed support 3d) Determine the state of stress at point A on the cross-section. Point A is located in the centre of the top flange at the fixed support. Present your answers on a 2D "stress element" Thin-Walled Section: d b 80 mm 50 mm 50 mm Loading and Reaction Diagram: "CHE 3 m

A 3m-long, thin-walled section (thickness t = 4 mm, for all elements) is used as a cantilever to support a point load P=2 kN. The point load P acts through the centroid of the cross-section (point c). The section's centreline dimensions are shown, and the moment of inertia about the x-axis is Ixx = 1.94 x 106 mm*. 3a) Determine the horizontal location of the centroid (i.e. calculate b) 3b) Determine the horizontal location of the shear centre (point o) (i.e. calculate d) 3c) Determine the values of the shear force (V), bending moment (M), and torque (7) at the fixed support 3d) Determine the state of stress at point A on the cross-section. Point A is located in the centre of the top flange at the fixed support. Present your answers on a 2D "stress element" Thin-Walled Section: d b 80 mm 50 mm 50 mm Loading and Reaction Diagram: "CHE 3 m

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Members with compression and bending

Compression members are structural elements that carry compressive axial force. They are the vertical members of a building that support beams and their design, which is governed by buckling and strength. Columns are known as struct or compression members, which are subjected to compressive forces. These members provide stiffness to the building and avoid any imperfection regarding the transfer of axial load. For instance, webs in a truss, braces in a framed structure, tiers, and so on.

Question

A 3m-long, thin-walled section (thickness t = 4 mm, for all elements) is used as a cantilever to
support a point load P=2 kN. The point load P acts through the centroid of the cross-section (point
c). The section's centreline dimensions are shown, and the moment of inertia about the x-axis is
Ixx = 1.94 x 106 mmª.
3a) Determine the horizontal location of the centroid (i.e. calculate b)
3b) Determine the horizontal location of the shear centre (point o) (i.e. calculate d)
3c) Determine the values of the shear force (V), bending moment (M), and torque (7) at the fixed
support
3d) Determine the state of stress at point A on the cross-section. Point A is located in the centre of
the top flange at the fixed support. Present your answers on a 2D "stress element"
Thin-Walled Section:
0
d
80 mm
50 mm
50 mm
X
Loading and Reaction Diagram:
T
M
"CHE
3m

A line is inscribed on a 3 mm thick steel alloy plate with an elastic modulus E = 200 GPa and shear
modulus G = 70 GPa. The plate is then loaded as shown below.
2a) Determine the slope of the line after the plate has been loaded
2b) Determine the reduction in thickness of the plate (in mm) under the applied loads
2c) If the plate has a yield stress = 300 MPa, determine the factor of safety against failure
according to the Maximum Normal Strain (St. Venant's) Criterion
Steel Alloy Plate:
y
line
250 mm
k
Į
50 kN
70 mm
↑
70 mm
100 KN
125 mm

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Step 2 The horizontal location of the centroid, b

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Step 3 The horizontal location of the shear center, d

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Step 4 Shear force (V), bending moment (M), and torque (T)

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