(a) Explanation Given that the total length of the beam is L = 4 m . The supporting points where the reaction force exerted on the beam are R I and R II . At the supporting side A is resolved into two components are A x and A y . The distance of the reaction force from the side A is a . The free-body diagram corresponding to the arrangement of the beam is given in Figure 1. Write the equation for the reaction force acting on the beam to corresponding region R I (Refer Fig 1). R I = 1 2 w A L I (I) Here, the force acting on the beam to the region I is R I , load per unit length acting on the side A is w A , and the distance of the beam to the region I on the side A is L I . Write the equation for the force acting on the beam to corresponding region R II (Refer Fig 1). R II = 1 2 w B L II (II) Here, the force acting on the beam to the region II is R II , and the distance of the beam to the region II on the side B is L II , and load per unit length acting on the side B is w B . Write the equilibrium equation for the section of beam and calculate the moment labeled at point A (Refer Fig 1). ∑ M A = 0 − R I ( a 3 ) − R II ( 8 + a 3 ) + B y ( L ) = 0 (III) Here, the distance between the region R I to the side A is a , the co-ordinates on the region R II to the side B is B y , and total length of the beam is L . Conclusion: Substitute a for L I and 1800 N/m for w A in equation (I) and solve for R I . R I = 1 2 ( 1800 N/m ) ( a m ) = ( 900 a ) N Substitute 4 − a for L II and 600 N/m for w B in equation (II) and solve for R II (b) To determine The reaction force exerted on the beam to supports at the side A B .

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 5.3, Problem 5.75P

(a)

To determine

The distance of the reaction force supports at the point A.

(b)

To determine

The reaction force exerted on the beam to supports at the side AB.

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Chapter 5.3, Problem 5.74P

Chapter 5.3, Problem 5.76P

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The distance of the reaction force supports at the point A .

Solution Summary: The free-body diagram corresponding to the arrangement of the beam is given in Figure 1.

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The distance of the reaction force supports at the point A.

The reaction force exerted on the beam to supports at the side AB.

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Chapter 5 Solutions