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A cantilevered beam of length L is subjected to axial and transverse loads. Figure 5.34 depiets the cross-section of the beam: an aluminum rectangular box of height h = 0.30 m, width b = 0.15 m, flange thickness ta = 12 mm, and web thickness tw = 5 mm. The beam is reinforced by two layers of unidirectional composite material of thickness te = 4 mm. The Young's moduli for the aluminum and unidirectional composite are Ea Ec = 140 GPa, respectively. At a station along the span of the beam, an experimentalist hia measured the axial strains on the top and bottom flanges of the beam as etop %3D %3D = 73 GPa and %3D = -2560u and 3675 resSnectively Find the bending moment and axial force acting at that statio. %3D

A cantilevered beam of length L is subjected to axial and transverse loads. Figure 5.34 depiets the cross-section of the beam: an aluminum rectangular box of height h = 0.30 m, width b = 0.15 m, flange thickness ta = 12 mm, and web thickness tw = 5 mm. The beam is reinforced by two layers of unidirectional composite material of thickness te = 4 mm. The Young's moduli for the aluminum and unidirectional composite are Ea Ec = 140 GPa, respectively. At a station along the span of the beam, an experimentalist hia measured the axial strains on the top and bottom flanges of the beam as etop %3D %3D = 73 GPa and %3D = -2560u and 3675 resSnectively Find the bending moment and axial force acting at that statio. %3D

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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**Problem 5.7. Box Beam with Strain Gauges** A cantilevered beam of length \(L\) is subjected to axial and transverse loads. Figure 5.34 depicts the cross-section of the beam: an aluminum rectangular box of height \(h = 0.30 \, m\), width \(b = 0.15 \, m\), flange thickness \(t_a = 12 \, mm\), and web thickness \(t_w = 5 \, mm\). The beam is reinforced by two layers of unidirectional composite material of thickness \(t_c = 4 \, mm\). The Young's moduli for the aluminum and unidirectional composite are \(E_a = 73 \, GPa\) and \(E_c = 140 \, GPa\), respectively. At a station along the span of the beam, an experimentalist has measured the axial strains on the top and bottom flanges of the beam as \(\epsilon_{top} = -2560 \, \mu\) and \(\epsilon_{bot} = 3675 \, \mu\), respectively. Find the bending moment and axial force acting at that station. (Note: Figure 5.34 is not included here. It is assumed to be a detailed illustration of the cross-section of the beam mentioned in the text.)
Transcribed Image Text:**Problem 5.7. Box Beam with Strain Gauges** A cantilevered beam of length \(L\) is subjected to axial and transverse loads. Figure 5.34 depicts the cross-section of the beam: an aluminum rectangular box of height \(h = 0.30 \, m\), width \(b = 0.15 \, m\), flange thickness \(t_a = 12 \, mm\), and web thickness \(t_w = 5 \, mm\). The beam is reinforced by two layers of unidirectional composite material of thickness \(t_c = 4 \, mm\). The Young's moduli for the aluminum and unidirectional composite are \(E_a = 73 \, GPa\) and \(E_c = 140 \, GPa\), respectively. At a station along the span of the beam, an experimentalist has measured the axial strains on the top and bottom flanges of the beam as \(\epsilon_{top} = -2560 \, \mu\) and \(\epsilon_{bot} = 3675 \, \mu\), respectively. Find the bending moment and axial force acting at that station. (Note: Figure 5.34 is not included here. It is assumed to be a detailed illustration of the cross-section of the beam mentioned in the text.)
### Reinforced Cross-Sections **Fig. 5.33: Reinforced Rectangular Cross-Section** - This diagram illustrates a simple reinforced rectangular cross-section. - The rectangle has a width (b) and a height (h), with an internal depth (d) represented along the vertical axis. - The reinforcing elements, labeled \(E_1\) and \(E_2\), are positioned on the top and bottom edges of the rectangle. - The directional arrows, \(\overline{i_2}\) and \(\overline{i_3}\), indicate the orientation of forces acting along the top edge and side of the rectangle respectively. **Fig. 5.34: Cross-Section of a Reinforced Rectangular Box Beam** - This figure represents a more complex reinforced rectangular box beam. - The outer dimensions include width (b) and height (h), while the inner wall thickness is labeled \(t_w\). - The top and bottom flanges have thicknesses \(t_a\) and \(t_e\). - The internal structure provides extra support, which is indicated by the reinforcements at the top (\(\varepsilon_{\text{top}}\)) and bottom (\(\varepsilon_{\text{bot}}\)) edges. - Similar to Fig. 5.33, the directional arrows \(\overline{i_2}\) and \(\overline{i_3}\) show the orientation of forces acting on the beam. These diagrams are crucial for understanding the structural design principles involved in reinforced concrete engineering.
Transcribed Image Text:### Reinforced Cross-Sections **Fig. 5.33: Reinforced Rectangular Cross-Section** - This diagram illustrates a simple reinforced rectangular cross-section. - The rectangle has a width (b) and a height (h), with an internal depth (d) represented along the vertical axis. - The reinforcing elements, labeled \(E_1\) and \(E_2\), are positioned on the top and bottom edges of the rectangle. - The directional arrows, \(\overline{i_2}\) and \(\overline{i_3}\), indicate the orientation of forces acting along the top edge and side of the rectangle respectively. **Fig. 5.34: Cross-Section of a Reinforced Rectangular Box Beam** - This figure represents a more complex reinforced rectangular box beam. - The outer dimensions include width (b) and height (h), while the inner wall thickness is labeled \(t_w\). - The top and bottom flanges have thicknesses \(t_a\) and \(t_e\). - The internal structure provides extra support, which is indicated by the reinforcements at the top (\(\varepsilon_{\text{top}}\)) and bottom (\(\varepsilon_{\text{bot}}\)) edges. - Similar to Fig. 5.33, the directional arrows \(\overline{i_2}\) and \(\overline{i_3}\) show the orientation of forces acting on the beam. These diagrams are crucial for understanding the structural design principles involved in reinforced concrete engineering.
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