Indeterminate structures A cantilever beam is supported by a cable at B. The beam and cable are both...

Question

Indeterminate structures A cantilever beam is supported by a cable at B. The beam and cable are both fabricated from Steel. The diameter of the cable is 5.0mm. The beam is a solid square cross-section, 50 X 50mm. You should assume that the cable does not have any slack before the load, P, is applied to the beam. You need to consider the deflection in the cable as the beam is loaded (it is non-zero). You have been tasked with analysing and optimising this structure for your client. To do this you must: a) Determine the tension force in the cable using the moment area method. Hint: You can determine the deflection at point B (in the rod and the beam) as a function of the unknown force and solve using displacement compatibility. b)Determine the tension force in the cable using energy methods. You do not need to consider the strain energy due to shear (this should be negligible). Comment on your answer and any differences observed compared with your answer to (a). c) Construct the shear force and bending moment diagrams and ensure that the beam and the cable can withstand the applied loading. Is the design safe? The material properties for Steel are: E 200.0 GPa v 0.28 ? 7.19 Mg/m3 sallow(tens XXXXXXXXXXMPa sallow(comp XXXXXXXXXXMPa tallow 130.0 MPa

Dr Shweta · Accepted Answer

Solution
Given: 
There is a cantilever beam which is supported by the cable at point B, both the beam and cable are fabricated from Steel, diameter of cable = 5.0mm, square cross-section area of beam = 50 X 50mm. deflection in the cable = 0 since the beam is loaded.
To find: 
a) tension force in the cable using the moment area method. 
b) tension force in the cable using energy methods 
c) Construct the shear force and bending moment diagrams and to find that is the design safe?
Solution: 
a) Calculation of tension force in the cable by moment area method. 
As we know that elongation of cable is calculated as:

Indeterminate structures A cantilever beam is supported by a cable at B. The beam and cable are both fabricated from Steel. The diameter of the cable is 5.0mm. The beam is a solid square...

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