An aluminum alloy [E = 10,300 ksi] tee‐shaped bar is used as a beam. The cross-section of the tee shape, shown in the figure below, has a total depth of d = 7.5 in. The centroidal z-axis of this cross-section is located 2.36 in. above point H. The beam spans in the x-direction and it bends about the z centroidal axis. A strain gage is affixed to the side of the tee stem at a distance c = 1.25 in. below the top surface of the tee shape. After loads are applied to the beam, a normal strain of ɛx = −810 μɛ is measured by the strain gage. What is the bending stress at point H?
An aluminum alloy [E = 10,300 ksi] tee‐shaped bar is used as a beam. The cross-section of the tee shape, shown in the figure below, has a total depth of d = 7.5 in. The centroidal z-axis of this cross-section is located 2.36 in. above point H. The beam spans in the x-direction and it bends about the z centroidal axis. A strain gage is affixed to the side of the tee stem at a distance c = 1.25 in. below the top surface of the tee shape. After loads are applied to the beam, a normal strain of ɛx = −810 μɛ is measured by the strain gage. What is the bending stress at point H?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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An aluminum alloy [E = 10,300 ksi] tee‐shaped bar is used as a beam. The
cross-section of the tee shape, shown in the figure below, has a total depth
of d = 7.5 in. The centroidal z-axis of this cross-section is located 2.36 in.
above point H. The beam spans in the x-direction and it bends about the z
centroidal axis. A strain gage is affixed to the side of the tee stem at a
distance c = 1.25 in. below the top surface of the tee shape. After loads are
applied to the beam, a normal strain of ɛx = −810 μɛ is measured by the
strain gage. What is the bending stress at point H?
Transcribed Image Text:The image depicts a diagram of an I-beam section with labeled dimensions and a strain gauge. The key elements are as follows:
- **I-beam Structure**: The drawing represents the cross-section of an I-beam, which is a common structural element used in construction and engineering.
- **Strain Gauge**: Positioned on the upper flange of the I-beam, labeled as "Strain gage." It is indicated by an arrow pointing to its location.
- **Dimensions**:
- **c**: The thickness of the flange at the top where the strain gauge is attached.
- **d**: The overall vertical depth of the I-beam.
- **H**: Represents the horizontal width of the bottom flange of the I-beam.
- **Axes**:
- **y-axis**: Represents the vertical axis in the diagram.
- **z-axis**: Represents the horizontal axis, located at the centroid of the I-beam.
This diagram illustrates how a strain gauge can be positioned to measure the deformation or strain on structural elements under load. The different axes and dimensions assist in defining the orientation and scale of the strain gauge placement and the structural member’s geometry.
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