Members AD, DC and ABC are assumed to be solid rigid members; member ED is a cable. For this structure, determine the reaction at A, the tension on cable ED and the force in member DC.

Question

Link for the structure: https://drive.google.com/file/d/1DxMIGWG2rRfqXvjci6aN2CHWfTkghlyP/view?usp=sharing

Answer 1

Let us proceed to calculate the requested forces (all units are N):

Reactions at Points A and E both have horizontal and vertical components.  At point E, the cable can ONLY be in tension, so components are vertical (up, positive), and horizontal (to the left, negative).  

1. Draw the FBD diagram of the entire truss system; sum moments about Pt. A to calculate reaction component E_h = -833.33 (to the left).
2. By similar triangle proportions, E_v= +625 (up).
3. Summing system horizontal forces, A_h = +833.33 (to the right).
4. By summing vertical forces of the entire system, A_v = +275 (up).
5. Using the Pythagorean Theorem and the above calculated reaction components at Pt.E, the calculated force in cable member DE = +1041.67 (tension).
6. Let us choose the Method of Joints to verify ALL member loads.  Recognize that there is an applied force to the span of member AC.  This translates to internal member shear forces which must be accounted for, which eventually contribute additional vertical loading at joints A and C.
7. Beginning at joint C, balance all joint loading (including contribution from member AC vertical shear force = -33.33, down).  Transfer calculated component forces to adjacent joints.  Balance ALL joint loadings throughout.
8. We calculate the tension components of member CD to be:  horizontal = -555.56 (to the left), vertical = +833.33 (up).  Using the Pythagorean Theorem, we calculate the force in member CD = +1001.54 (tension).
9. Additionally, forces in member AC = -555.56 (compression), and in member AD = -347.22 (compression).

In summary, the requested load values per the problem statement are:

Reaction at Pt.A….A_h = +833.33 (to the right)

             A_v = +275 (up)

Cable member DE = +1041.67 (tension)

Rigid member CD  = +1001.54 (tension)

Please contact me for a more detailed explanation, setup and walkthrough of the joint isolation diagram, and step-by-step joint load balancing calculation.