A point load of 2.236kN is applied at point 3 of a frictionless pin- jointed structure which consists of members as shown in Fig Q2. Displacements at point 1 are fixed in x and y directions whereas only displacement in y direction is fixed at point 2. Member 1 has end points 1 and 2, member 2 has end points 2 and 3 and member 3 has end points 1 and 3. The cross sectional areas of member 1, 2 and 3 are 500 mm², 250 mm² and 1414.42 mm² respectively. Length of both member 1 and 2 is 10 m. Young's modulus (E) for all members is 200,000 N/mm². 2.236 KN 2 Fig Q2: Pin-jointed structure (b) Calculate horizontal and vertical displacements at point 2 and point 3.

Mechanics of Materials (MindTap Course List)
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Chapter2: Axially Loaded Members
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A point load of 2.236kN is applied at point 3 of a frictionless pin-
jointed structure which consists of members as shown in Fig Q2.
Displacements at point 1 are fixed in x and y directions whereas only
displacement in y direction is fixed at point 2.
Member 1 has end points 1 and 2, member 2 has end points 2 and 3
and member 3 has end points 1 and 3. The cross sectional areas of
member 1, 2 and 3 are 500 mm², 250 mm² and 1414.42 mm²
respectively. Length of both member 1 and 2 is 10 m. Young's
modulus (E) for all members is 200,000 N/mm².
N
117
2.236 KN
Fig Q2: Pin-jointed structure
(b)
Calculate horizontal and vertical displacements at point 2 and
point 3.
Element stiffness (ke) matrix of a pin-jointed element is:
cos²
[k]-(45)
A.E cos sin
-cos²
cos sin
sin²
-cos sin
-cos²
-cos sin
- cosesin
- sin²
cos²
cos sin
-cos sin
sin² 0
cos sin
sin²
Subscript 'e' stands for element, L is length of an element, e is the
angle of inclination of the element measured anti-clockwise from the
x-axis.
Transcribed Image Text:A point load of 2.236kN is applied at point 3 of a frictionless pin- jointed structure which consists of members as shown in Fig Q2. Displacements at point 1 are fixed in x and y directions whereas only displacement in y direction is fixed at point 2. Member 1 has end points 1 and 2, member 2 has end points 2 and 3 and member 3 has end points 1 and 3. The cross sectional areas of member 1, 2 and 3 are 500 mm², 250 mm² and 1414.42 mm² respectively. Length of both member 1 and 2 is 10 m. Young's modulus (E) for all members is 200,000 N/mm². N 117 2.236 KN Fig Q2: Pin-jointed structure (b) Calculate horizontal and vertical displacements at point 2 and point 3. Element stiffness (ke) matrix of a pin-jointed element is: cos² [k]-(45) A.E cos sin -cos² cos sin sin² -cos sin -cos² -cos sin - cosesin - sin² cos² cos sin -cos sin sin² 0 cos sin sin² Subscript 'e' stands for element, L is length of an element, e is the angle of inclination of the element measured anti-clockwise from the x-axis.
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