A truss is shown in the figure below with a load of 10 kN acting
A truss is shown in the figure below with a load of 10 kN acting vertically downward at point E. Support A is pinned while support C is a roller support.
Choose the correct statements:
A. There are no zero force members in the truss
B. The member AE is in compression
C. The force in the member BE is 10 kN (compression)
D. Member AB is a zero force member.
Please scroll down to see the correct answer and solution guide.
Right Answer is:
SOLUTION
Calculation:
First to determine the support reactions:
∑ MA = 0 ⇒ RC × 6 – 10 × 3 = 0 ⇒ RC = 5 kN
∑ FY = 0 ⇒ RC + RA -10 = 0 ⇒ RA = 5 kN
(positive reaction indicates upward direction as per our convention)
The support at C is a roller support, so the reaction at C will only be in the vertically upward direction, so there must not be any force in the member BC, otherwise the support C won’t remain balanced. Hence member BC is a zero force member. Hence option a) is incorrect.
At A,
RA + FAE × sin θA = 0
⇒ FAE = -5 × 5/4 = -25/4 = -6.25 (6.25 kN compression)
FAE × cos θA + FAB = 0
⇒ FAB = 6.25 × 3/5 = 3.75 (3.75 kN tension)
∴ member AB is not a zero force member.
Hence option b) is correct and d) is incorrect.
At E,
Member AE and DE are in the same line while the load 10 kN and the member BE being in the same line. So magnitude and nature of force in member AE and DE will be same. So without solving anything the member force in BE can be found as 10 kN compression.
We can also find this by solving the joint as well. The image is the Free body diagram at joint E.
⇒ 10 + FBE = 0 ⇒ FBE = -10 kN (compression)
∴ option c) is correct.
