# Direction of normal reactions on a beam

1. Jun 10, 2013

### arestes

1. The problem statement, all variables and given/known data
Problem 10.36 The bar has cross-sectional areaAand
modulus of elasticity E. If an axial force F directed toward
the right is applied atC, what is the normal stress in
the part of the bar to the left ofC? (Strategy: Drawthe
free-body diagram of the entire bar and write the equilibrium
equation. Then apply the compatibility condition
that the increase in length of the part of the bar to the left
of C must equal the decrease in length of the part to the
right of C.) SEE ATTACHED PDF

2. Relevant equations
sum of forces =0
Young's modulus definition for compatibility of deformations

3. The attempt at a solution
Solution is already in the pdf, I just don't understand why the reactions (normal forces) on the bar are both to the left. Normals are supposed to go towards the body. However, if I were to take the left reaction force going to the right (where I think it should point) the solution would be negative. Same happens with other lecture notes (page 6 here http://www.yamnuska.ca/student/smtl/notes/StaticIndetermW06.pdf ) . What am I doing wrong?

#### Attached Files:

• ###### hw06.pdf
File size:
1 MB
Views:
935
Last edited: Jun 10, 2013
2. Jun 10, 2013

### SteamKing

Staff Emeritus
These forces are reactions. It's not clear why you are calling reactions 'normal forces'.
It is not made very clear in the problem statement, but the bar must be built in or fixed at each end.
With the axial force applied at point C, if one were to make a cut in the bar just to the right of C and draw the resulting FBD, then it is clear that the reaction at the left end of the bar must be in the opposite direction to the axial force at C. Similarly, if a cut is made in bar to the left of C, then drawing the FBD will show that the reaction at the right end of the bar must also point to the left, in order for equilibrium to exist.