   Chapter 1, Problem 1.3.3P 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 xdirection ,

Fx=0100+50+Bx=0Bx=50 lb

Now take equilibrium of moments about A,

MA=0100+By×20=0By=5 lb

Take equilibrium of forces in ydirection,

Fy=0Ay+By=0Ay=By=(5)=5Ay=5 lb

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

Take equilibrium of forces in xdirection ,

Fx=0Cx=BxCx=50 lb

Take equilibrium of forces in ydirection,

Fy=0Cy=0

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

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