Slide 1

Example A

Draw the FBD of the platform and solve the unknown reactions on it.The weight of the platform is 1967N.G701.4m0.8m1.0mABT = tensionW = weight of platfromAx = horizontal reaction at AAy = vertical reaction at AG701.4m0.8m1.0mABAxAyTWFBD of platformES 11 ENGINEERING STATICS6/30/2015rjsg1Solution (scalar approach)

G701.4m0.8m1.0mABAxAyTWFBD of platformES 11 ENGINEERING STATICS6/30/2015rjsg2

G701.4m0.8m1.0mABAxAyTWFBD of platformSolution (scalar approach)ES 11 ENGINEERING STATICS6/30/2015rjsg3G701.4m0.8m1.0mABAxAyTWFBD of platform

Solution (scalar approach)ES 11 ENGINEERING STATICS6/30/2015rjsg4

G701.4m0.8m1.0mABAxAyTWFBD of platform

Solution (vector approach)ES 11 ENGINEERING STATICS6/30/2015rjsg5

G701.4m0.8m1.0mABAxAyTWFBD of platformSolution (vector approach)ES 11 ENGINEERING STATICS6/30/2015rjsg6Example BThe link shown is pin connected at A and rests against a smooth support at B. Compute the vertical and horizontal reaction at the pin A.

FBD of linkES 11 ENGINEERING STATICS6/30/2015rjsg7Solution

FBD of linkES 11 ENGINEERING STATICS6/30/2015rjsg8

SolutionES 11 ENGINEERING STATICS6/30/2015rjsg9

FBD of linkSolutionES 11 ENGINEERING STATICS6/30/2015rjsg10Example CThe lever ABC is pin-supported at A and connected to a short link BD as shown. The weight of the members are negligible. Determine the reaction of the pin to the lever at A.

ES 11 ENGINEERING STATICS6/30/2015rjsg11Solution

FBD of lever(3-force body)

FBD of link(two-force body)ES 11 ENGINEERING STATICS6/30/2015rjsg12

FBD of lever(3-force body)

FAF40045

15.2645

SolutionES 11 ENGINEERING STATICS6/30/2015rjsg13Example D

A sign of uniform density weighs 270 lb and is supported by a ball-and-socket joint at A and by two cables.Determine the tension in each cable and the reaction at A.SOLUTION:Create a free-body diagram for the sign.Apply the conditions for static equilibrium to develop equations for the unknown reactions.ES 11 ENGINEERING STATICS14Solution

Create a free-body diagram for the sign.Since there are only 5 unknowns, the sign is partially constrain. It is free to rotate about the x axis. It is, however, in equilibrium for the given loading.

ES 11 ENGINEERING STATICS15

Apply the conditions for static equilibrium to develop equations for the unknown reactions.

Solve the 5 equations for the 5 unknowns,SolutionES 11 ENGINEERING STATICS16The homogenous plate shown has a mass of 100kg and is subjected to a force and couple moment along its edges. If it is supported in the horizontal plane by means of a roller at A, a ball-and-socket joint at B, and a cord at C, determine the reactions at the supports.

Example EES 11 ENGINEERING STATICS17Solution (vector approach)

FBD of plateES 11 ENGINEERING STATICS18

Solution (vector approach)ES 11 ENGINEERING STATICS19

Solution (vector approach)ES 11 ENGINEERING STATICS20

FBD of plate

Solution (vector approach)ES 11 ENGINEERING STATICS21ABCDxyz1.5m0.5m0.5m0.5m0.25mExample FThe member is supported by a smooth hinge at A and cable BC. If the load at D is 10 N, determine the tension in the cable and the components of the reaction at A.ES 11 ENGINEERING STATICS22Solution (vector approach)

ABCxyz1.5m0.5m0.5m0.5m0.25m

FBD of member10 NES 11 ENGINEERING STATICS23

Solution (vector approach)ES 11 ENGINEERING STATICS24

Solution (vector approach)ES 11 ENGINEERING STATICS25ABCxyz1.5m0.5m0.5m0.5m0.25m

FBD of member10 N

Solution (vector approach)ES 11 ENGINEERING STATICS26Homework (due July 1)The windlass shown is supported by a thrust bearing at A and a smooth journal bearing at B, which are properly aligned on the shaft. Determine the magnitude of the vertical force P that must be applied to the handle to maintain equilibrium of the 100-kg bucket.

ES 11 ENGINEERING STATICS27