(a) Explanation Refer Fig P7.91. Sketch the free body diagram for the section DE of fig P7.91. Write the condition to find the shear at E. Σ M D = 0 (I) Here, Σ M D is the net moment at D. Write the condition to find the shear at D. Σ F y = 0 (II) Here, Σ F y is the net force in the y direction. Conclusion: The counter clockwise direction is taken as positive and the clockwise direction is taken as negative. Refer figure 1 and use equation (I) to find the shear at E. Σ M D = 0 235 kip ⋅ ft − 172 kip ⋅ ft − ( 6 kip ) ( 1.5 ft ) − V E ( 3 ft ) = 0 V E = 18 kips (III) Refer figure 1 and use equation (II) to find the shear at D. Σ F y = 0 − 6 kips − 18 kips − V D = 0 V D = 24 kips (IV) In order to draw the shear diagram and the moment diagram, the steps are as follows: The values of shear and moment are plotted at D and E using equation (III) and (IV). In the shear diagram, the portion CDEF is a straight line as w is a constant. The moment at C and F are calculated using the area under the shear diagram. As the moment at A, M A = 0 , and the moment at C, M C = 147 kips ⋅ ft , the shear diagram for AC also has an area of 147 kips ⋅ ft . The slope of the shear diagram is − 2 kips/ft since the distributed load extends over entire beam. Sketch the diagram for AC and thus, find the value of P (b) To determine To draw the shear and bending moment diagrams for the beam.

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Chapter 7.3, Problem 7.92P

(a)

To determine

The value of P and Q.

(b)

To determine

To draw the shear and bending moment diagrams for the beam.

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Chapter 7.3, Problem 7.91P

Chapter 7.4, Problem 7.93P

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The value of P and Q .

Solution Summary: The author illustrates the value of P and Q in Fig. P7.91. Write the condition to find the shear at E.