Tension in a cable supporting a hinged beam

  • Thread starter adlewis90
  • Start date
  • #1
2
0
I have tried to complete the following question by taking moments about point A, but to no avail. Could anybody help me with where i am going wrong. Do I need to include perpendicular distance?

The I-beam A-B shown below is supported by a cable at B and a pin at A. The cable is inclined at an angle, θ = 21° to the longitudinal axis of the beam. The beam supports a load, m, of 12 kN at a distance mx = 1.5 m from B.

example_zpsed2967d3.png


If the mass of the beam is 95 kg/m and its total weight can be assumed to act through the centre of gravity of the beam, calculate:

a) the cable tension, T

b) the resultant force acting on the pin at A.

Given:

Ax = 0.12 m, Beam Depth, D = 0.5 m, Beam Length, L = 5 m, Gravity, g = 9.81 m/s2



Part a)

Weight of beam = 4.65975 kN

By taking moments about A, T = 26.09±0.2 kN

Part b)

To determine the resultant at A, calculate the horizontal and vertical reactions AH and AV respectively:

AH = 24.36±0.2 kN

AV = 7.31±0.2 kN

Therefore, the resultant (using Pythagoras), R = 25.43±0.2 kN
Incorrect

Here is my solution to the cable tension

(4.88)(T)(sin21)+(111.834x0.06)-(4.5479x10^3)(2.44)-(12x10^3)(3.38)=0

1.7488(T)=+6.7098+11.0968x10^3+40.56x10^3

1.7488(T)=51650.0902

(T)= (51.65x10^3)/1.7488 =29.53kn
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,874
1,655
I have tried to complete the following question by taking moments about point A, but to no avail. Could anybody help me with where i am going wrong. Do I need to include perpendicular distance?
You need to show your working. i.e. how did you compute the moments?
It helps to do the algebra with the variables first and then plug the numbers in.
If you didn't take into account the beam "depth" D, you should give that a try.
Use the model answer to clue you in to how far out you are.
 
Last edited:
  • #3
2
0
Sorted the question before looking on here, was simply solved by extending the length of the cable to where it intersected the centreline of the beam and using this point in the x axis as the distance. Thanks for your help
 

Related Threads on Tension in a cable supporting a hinged beam

  • Last Post
Replies
2
Views
12K
  • Last Post
Replies
1
Views
8K
  • Last Post
Replies
6
Views
653
Replies
9
Views
309
Replies
4
Views
2K
Replies
1
Views
6K
Replies
7
Views
4K
  • Last Post
Replies
10
Views
10K
Replies
11
Views
12K
Replies
1
Views
5K
Top