In Figure Q4a, AC is a beam is supported at A and C with a uniformly distributed load of 40 kN/m between A and B. The distance A to B is d₁ with a length of 12.00 m; the distance B to C is d₂ with a length of 6.00 m. The point M is located at the mid-point of the beam AC. A UDL C d1 M B d2 Figure Q4a a) Draw and label the shear force diagram (SFD) for the beam shown in Figure Q4a. Label the values for shear force and bending moment at points A, B, C and at the mid-point M. [7 marks] b) Draw and label the bending moment diagram (BMD) for the beam shown in Figure Q4a and clearly indicate the type of bending that occurs between AB and between BC. On your diagram, clearly show the value of the maximum bending moment and where it occurs along the beam terms of the distance from A. In addition, label the values for bending moment at points A, B, C and at the mid-point M. [8 marks] c) The diameter (d) of a solid rod (i.e., with a circular cross-section) is 14 mm and is made from a homogeneous material. The length (L) of the rod is 1.75 m and Young's Modulus for the material (E) is 375 GPa. When the rod is placed under tension it experiences deformation and a stress (σ) of 850 MPa. Calculate the following: (i) Strain energy (U) to 2 decimal places in Joules. (ii) Strain energy per unit volume (U/V) in J/m³.to 2 decimal places. The change in length AL to 2 decimal places in mm. (!!!) (iv) The strain (ε) due to deformation to 2 significant figures. [10 marks]

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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In Figure Q4a, AC is a beam is supported at A and C with a uniformly distributed load of
40 kN/m between A and B. The distance A to B is d₁ with a length of 12.00 m; the distance
B to C is d₂ with a length of 6.00 m. The point M is located at the mid-point of the beam
AC.
A
UDL
C
d1
M
B
d2
Figure Q4a
a) Draw and label the shear force diagram (SFD) for the beam shown in Figure Q4a.
Label the values for shear force and bending moment at points A, B, C and at the
mid-point M.
[7 marks]
b) Draw and label the bending moment diagram (BMD) for the beam shown in
Figure Q4a and clearly indicate the type of bending that occurs between AB and
between BC. On your diagram, clearly show the value of the maximum bending
moment and where it occurs along the beam terms of the distance from A. In
addition, label the values for bending moment at points A, B, C and at the mid-point
M.
[8 marks]
c) The diameter (d) of a solid rod (i.e., with a circular cross-section) is 14 mm and is
made from a homogeneous material. The length (L) of the rod is 1.75 m and
Young's Modulus for the material (E) is 375 GPa. When the rod is placed under
tension it experiences deformation and a stress (σ) of 850 MPa. Calculate the
following:
(i) Strain energy (U) to 2 decimal places in Joules.
(ii) Strain energy per unit volume (U/V) in J/m³.to 2 decimal places.
The change in length AL to 2 decimal places in mm.
(!!!)
(iv)
The strain (ε) due to deformation to 2 significant figures.
[10 marks]
Transcribed Image Text:In Figure Q4a, AC is a beam is supported at A and C with a uniformly distributed load of 40 kN/m between A and B. The distance A to B is d₁ with a length of 12.00 m; the distance B to C is d₂ with a length of 6.00 m. The point M is located at the mid-point of the beam AC. A UDL C d1 M B d2 Figure Q4a a) Draw and label the shear force diagram (SFD) for the beam shown in Figure Q4a. Label the values for shear force and bending moment at points A, B, C and at the mid-point M. [7 marks] b) Draw and label the bending moment diagram (BMD) for the beam shown in Figure Q4a and clearly indicate the type of bending that occurs between AB and between BC. On your diagram, clearly show the value of the maximum bending moment and where it occurs along the beam terms of the distance from A. In addition, label the values for bending moment at points A, B, C and at the mid-point M. [8 marks] c) The diameter (d) of a solid rod (i.e., with a circular cross-section) is 14 mm and is made from a homogeneous material. The length (L) of the rod is 1.75 m and Young's Modulus for the material (E) is 375 GPa. When the rod is placed under tension it experiences deformation and a stress (σ) of 850 MPa. Calculate the following: (i) Strain energy (U) to 2 decimal places in Joules. (ii) Strain energy per unit volume (U/V) in J/m³.to 2 decimal places. The change in length AL to 2 decimal places in mm. (!!!) (iv) The strain (ε) due to deformation to 2 significant figures. [10 marks]
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