Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
5th Edition
ISBN: 9780073398006
Author: Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher: McGraw-Hill Education
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Chapter 5, Problem 1P

(a)

To determine

Provide the equations for shear and moment between points B and C as a function of x for origin of x at point A.

(a)

Expert Solution
Check Mark

Answer to Problem 1P

The shear between points B and C as a function of x for origin of x at point A is V=14kips_.

The equation for moment between points B and C as a function of x for origin of x at point A is M=8014xkipft_.

Explanation of Solution

Apply the sign conventions for calculating reactions using the three equations of equilibrium as shown below.

  • For summation of forces along x-direction is equal to zero (Fx=0), consider the forces acting towards right side as positive (+) and the forces acting towards left side as negative ().
  • For summation of forces along y-direction is equal to zero (Fy=0), consider the upward force as positive (+) and the downward force as negative ().
  • For summation of moment about a point is equal to zero (Matapoint=0), consider the clockwise moment as positive and the counter clockwise moment as negative.

Let Ay be the vertical reactions at the hinged support A and Cy be the vertical reaction at the roller support C.

Sketch the free body diagram of the beam as shown in Figure 1.

Fundamentals of Structural Analysis, Chapter 5, Problem 1P , additional homework tip  1

Refer to Figure 1.

Use equilibrium equations:

Summation of moments about A is equal to 0.

MA=025+15×30+0.5×10×(20+102)Cy×20+8×10=0Cy=34kips()

Summation of forces along y-direction is equal to 0.

+Fy=0Ay+3480.5×1015=0Ay=6Ay=6kips()

Consider a section at a distance x from A.

Sketch the section at a distance x from A between B and C as shown in Figure 2.

Fundamentals of Structural Analysis, Chapter 5, Problem 1P , additional homework tip  2

Refer to Figure 2.

Summation of forces along y-direction is equal to 0.

+Fy=068V=0V=14kips

Hence, the shear between points B and C as a function of x for origin of x at point A is V=14kips_.

Summation of moments about A is equal to 0.

MA=0M+(14)×x+8×10=0M=8014xkipft

Hence, the equation for moment between points B and C as a function of x for origin of x at point A is M=8014xkipft_.

(b)

To determine

Provide the equations for shear and moment between points B and C as a function of x for origin of x at D.

(b)

Expert Solution
Check Mark

Answer to Problem 1P

The shear between points B and C as a function of x for origin of x at D is V=14kips_.

The equation for moment between points B and C as a function of x for origin of x at D is M=14x340kipft_.

Explanation of Solution

Calculation:

Refer to part (a),

The reactions at supports.

Ay=6kips()Cy=34kips()

Consider a section at a distance x from D.

Sketch the section at a distance x from D between B and C as shown in Figure 3.

Fundamentals of Structural Analysis, Chapter 5, Problem 1P , additional homework tip  3

Refer to Figure 3.

Summation of forces along y-direction is equal to 0.

+Fy=0150.5×10+34+V=0V=14kips

Hence, the shear between points B and C as a function of x for origin of x at D is V=14kips_.

Summation of moments about D is equal to 0.

MD=0M+(14)×x+34×100.5×10×102+25=0M=14x340kipft

Therefore, the equation for moment between points B and C as a function of x for origin of x at D is M=14x340kipft_.

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