**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.

Axial force: The force exerted on a body in its transverse direction. It is a pulling factor that…

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

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 6. A three-block composite structure is loaded through rigid end plates, as s in the figure. What…

A: To find position of x such that end plates remain horizontal

Q: Problem 2. A W12×58 acts compositely with a 5-inch-thick concrete slab. The effective slab width is…

Q: 2. In the figure shown, a. What is the distance of the centroid of the composite section from the…

Q: Aluminum A = 1.25 in.? E = 10 x 106 psi Steel A = 2.0 in.2 E= 29 x 10° psi 15 in- -12 in.-

A: The given data is: For Aluminum bar: Length = 15 in Area = 1.25 in2 Modulus of Elasticity (E) = 10 x…

Q: SITUATION 1. A composite bar is made by attaching a copper rod of length 900 mm and diameter 30 mm…

Q: The composite bar shown is fixed at the ends and is subjected to the axial load P shown. If the…

Q: determine the modular ratio n. Enter your answer to 4 decimal places.

Q: find the moment of inertia of the composite area shown in the figure below. For the X- Y centroidal…

A: Following figure of the composite area is given, it is required to determine the moment of inertia…

Q: A composite assembly consisting of a steel [G = 80 GPa] core (2) connected by rigid plates at the…

A: This question is related to the Strength of Material from Civil Engineering.

Question

100%

**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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1 Introduction

VIEW

Step 2 Given Data

VIEW

Step 3 Bending moment and axial force acting at the station

VIEW

Step 4 Conclusion

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

= 12 mm. The The following figure depicts an aluminum I beam of height h = 0.25 m, width b = 0.2 m, flange thickness ta = 16 mm, and web thickness tw beam is reinforced by two layers of unidirectional composite material of thickness to = 5 mm. The section is subjected to an axial force N₁ = 500 kN. The Young's moduli for the aluminum and unidirectional composite are Ea 73 GPa and Ec 140 GPa, respectively. = (a) Compute the axial stiffness for this structure. (b) Compute the maximum axial stress in both the aluminum and composite layers. CS Scanned with CamScanner 1₁ I h t₂ I b po
A composite beam made of steel and bronze has the cross section shown. The cross-sectional dimensions are b1 = 0.5 in, b2 = 1.5 in., and d = 1.0 in. The elastic modulus of the steel is E1 = 30,000 ksi, and its allowable bending stress is 24 ksi. The elastic modulus of the bronze is E, = 15,000 ksi, and its allowable bending stress is 16 ksi. Calculate the magnitude of the allowable bending moment that can be applied about the z centroidal axis. y Bronze (2) Steel (1) bị b2 Answer: M = i Ib-in. Save for Later Attempts: 0 of 1 used Submit Answer
Bar A-B-C is made from a fully bonded composite of two materials as shown in the cross section below. Find the Z displacement at point C. A C 1.10 m 20 kN B 1.25 m 50 kN с Y I cross section c-c Uz = 5 mm, material 1 5 mm, material 2 5 mm, material 1 25 mm Material 1 E = 240 (GPa) Material 2 E = 180 (GPa) mm (at C)
A rectangular steel bar with given dimensions is subjected to a axial compression. What is the critical buckling load? width, b = 42 mm thick, t = 60 mm L = 3.25 E = 180 Gpa
4