GATE ME 2019 Set 1 — Question 48
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Engineering Mechanics → Statics → Trusses (Joints & Sections)
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Question
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is ______
Correct answer
4.98 to 5.02
Solution
1.Analyze the overall equilibrium of the truss:
Due to the symmetry of the truss and the loading, the vertical reactions at the supports and are equal:2.Analyze joint B:
Joint is a connection between members , , and . Since there is no vertical external load or reaction at joint , the vertical member must be a zero-force member to satisfy vertical equilibrium (). Thus, .For horizontal equilibrium at joint : .
3.Analyze joint C:
The forces acting at joint are the reaction kN (upwards), the force in member (, horizontal), and the force in member (, at to the horizontal).For vertical equilibrium at joint :
4.Calculate the force in member BC:
For horizontal equilibrium at joint :Therefore, the magnitude of the force in member is 5 kN.
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