2. The component shown always breaks at point C, which is just to the right of thecontact point of the roller at B. Find the internal forces in terms of shear, normal andbending to show why this is.150mm-250 mm-400 NOB125 mm500 N110 mm80 N•m

Answered: 2. The component shown always breaks at…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.19P: During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as...

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Question

2. The component shown always breaks at point C, which is just to the right of the
contact point of the roller at B. Find the internal forces in terms of shear, normal and
bending to show why this is.
150
mm
-250 mm-
400 N
OB
125 mm
500 N
110 mm
80 N•m

Expert Solution

Step 1

The component always breaks at point C, which is just right of the contact point of the roller at B. So, draw the free-body diagram of the section which is just right of the contact point of the roller at B as follows:

Here, the reaction force at C in the horizontal direction is R_Cx, the reaction force at C in the vertical direction is R_Cyand the moment reaction at C is M_C.

Step 2

Consider the equilibrium of force in the horizontal direction,

$\begin{array}{rcl} R_{C x} - 500 N & = & 0 \\ R_{C x} & = & 500 N \end{array}$

Consider the equilibrium of force in the vertical direction,

$\begin{array}{rcl} R_{C y} - 400 N & = & 0 \\ R_{C y} & = & 400 N \end{array}$

Calculate the moment reaction at C,

$\begin{array}{rcl} M_{C} - 400 N \times 250 mm + 500 N \times 125 mm - 80 N·m & = & 0 \\ M_{C} - 400 N \times 250 mm \frac{10^{- 3} m}{1 mm} + 500 N \times 125 mm \frac{10^{- 3} m}{1 mm} - 80 N·m & = & 0 \\ M_{C} - 400 N \times 0.250 m + 500 N \times 0.125 m - 80 N·m & = & 0 \\ M_{C} & = & 117.5 N·m \end{array}$

Step 3

Therefore, the internal forces in terms of shear, normal, and bending are,

$R_{C x} = 500 N (Normal) R_{C y} = 400 N (Shear) M_{C} = 117.5 N·m (Bending)$

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2. The component shown always breaks at point C, which is just to the right of the contact point of the roller at B. Find the internal forces in terms of shear, normal and bending to show why this is. 150 mm -250 mm- 400 N A OB 125 mm 500 N 110 mm 80 N•m