Chapter 1, Problem 1.3.3P

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

# Segments AB and BC of beam ABC are pin connected a small distance to the right of joint B (sec figure). Axial loads act at A and at the mid-span of AB. A concentrated moment is applied at joint B. (a) Find reactions at supports A, B, and C. (b) Find internal stress resultants N, V, and M at l5 ft.

To determine

You need to calculate external reaction forces at A, B and C; and the internal forces − axial force N, shear force V and bending moment M at 15 ft from A in the figure given below.

Explanation

Given Information:

The following figure is given:

Calculation:

Draw free body diagram of AB section as shown in figure below for external forces,

Take equilibrium of forces in xâˆ’direction ,

âˆ‘Fx=0â‡’âˆ’100+50+Bx=0â‡’Bx=50Â lb

Now take equilibrium of moments about A,

âˆ‘MA=0â‡’100+ByÃ—20=0â‡’By=âˆ’5Â lb

Take equilibrium of forces in yâˆ’direction,

âˆ‘Fy=0â‡’Ay+By=0â‡’Ay=âˆ’By=âˆ’(âˆ’5)=5â‡’Ay=5Â lb

Draw free body diagram of BC section as shown in figure below for external forces,

Take equilibrium of forces in xâˆ’direction ,

âˆ‘Fx=0â‡’Cx=Bxâ‡’Cx=50Â lb

Take equilibrium of forces in yâˆ’direction,

â€ƒâ€ƒâˆ‘Fy=0â‡’Cy=0

Now, draw free body diagram for internal reactions at 15 ft as shown in figure below,

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