10:48 AM @session.masteringengineering.com Problem 4.106 MasteringEngineering Ma

Question

10:48 AM @session.masteringengineering.com Problem 4.106 MasteringEngineering MasteringComputerScie… ..ooo Bell - Problem 4.106 The forces F! = {-5i + -4k} kN and F2 { 5i-4j-2k) kN act on the end of the beam. Replace these forces by an equivalent force and couple moment acting at point O 1150 mm F 50 mm 250 mm 4 m Tap image to zoom Part A Determine the resultant force Enter the , y, and z components of the force separated by commas using three significant figures. (FR),, (Fr)y, (FR)- kN Submit Give Up

Explanation / Answer

As,

F1 = - 5 i + 4 j - 4 k, {kN} and

F2 = 5 i - 4 j - 2 k       {kN}

>> Now, as resultant is Fr, and

Fr = F1 + F2

=> Fr = - 5 i + 4 j - 4 k + 5 i - 4 j - 2 k  

=>Fr = - 6 k

>> So, resultant force = - 6 k, i.e. it is only in -ve z-direction with magnitude 6 kN   ..ANSWER...

and from point O,

Vector from point O to point of application of force, i.e. point A, let it is at y distance from center line

as, coordinates of point A = (4,y,0.25)

>> As, point B = point of application of force F1 = (4,-0.15,0.25)

>> As, point C = point of application of force F2 = (4,0.15,0.25)

>> So, Mo = Moment of these two forces about O

=> So, OB X F1 + OC X F2

=> (4 i - 0.15 j + 0.25 k) X (- 5 i + 4 j - 4 k) + (4 i + 0.15 j + 0.25 k) X (5 i - 4 j - 2 k)

=> On simplifying,

Mo = 0.3 i + 24 j - 1.50 k

=> X-Component = 0.3 kN-m

=> Y-Component = 24 kN-m

=> Z-Component = - 1.50 kN-m

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