Q.3)A rigid bar DAB is supported by two circular rods and a pin as shown below.The member at D is an aluminum (E = 70 GPa) rod, and the member BC is asteel (E = 200 GPa) rod. The diameter of the aluminum rod is 10 mm and that ofthe steel rod is 5 mm. Calculate the average normal stresses in the steel andaluminum rods due to the applied load of 650 N. Also, determine the rotation ofthe rigid bar DAB about the pin A, and the horizontal displacement of point D.200 mmAB150 mm100 mm150 mm650 NDI50 mm

Equations of equilibrium : ∑MA=0650×250-FBC×150-FD×150=01083-FBC-FD=0…

Answered: A rigid bar DAB is supported by two…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Q.3)A rigid bar DAB is supported by two circular rods and a pin as shown below.
The member at D is an aluminum (E = 70 GPa) rod, and the member BC is a
steel (E = 200 GPa) rod. The diameter of the aluminum rod is 10 mm and that of
the steel rod is 5 mm. Calculate the average normal stresses in the steel and
aluminum rods due to the applied load of 650 N. Also, determine the rotation of
the rigid bar DAB about the pin A, and the horizontal displacement of point D.
200 mm
A
B
150 mm
100 mm
150 mm
650 N
DI
50 mm

Expert Solution

Step 1

Equations of equilibrium :

$\sum M_{A} = 0 650 \times 250 - F_{B C} \times 150 - F_{D} \times 150 = 0 1083 - F_{B C} - F_{D} = 0 \to e q . 1 C o m p a t i b i l i t y : δ_{B C} = δ_{D} \frac{F_{B C} \times 200}{22.5 \times 10^{- 6} \times 200 \times 10^{9}} = \frac{F_{D} \times 50}{40 \times 10^{- 6} \times 70 \times 10^{9}} F_{B C} = 0.40179 F_{D} \to e q . 2$

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