# E14 - Applied Mechanics: Statics - Stanford University

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e14 - applied mechanics: staticse14 - applied mechanics: staticsnohomeworkthis week ;-)fifthhomeworkduemon/wed/fri, 12:50-2:05pm, 370-370syllabusstatics of the leaning problemstatics of the leaning problem12FY 0 : BV - W 0BV WFY 0 :MB 0 : A d2 - W d1/2 0MA 0 : Bd2-w0d12/2 0A W d1/2d2F X 0 : A - BH 0BH W d1/2d2the flatter the leaning anglethe larger the horizontal force5. equations of equilibriumAV - w0d1 0AV w0d1B w0d12/2d2FX 0 :A - B 0AH w0d12/2d2the flatter the leaning anglethe larger the horizontal force5. equations of equilibrium

statics of the leaning problemstatics of the leaning problemFY 0 : AV W 0AV -WMA 0 : B d2 - W d1/2 0FY 0 : BV - W 0BV WMB 0 : A d2 - W d1/2 0A W d1/2d2B W d1/2d2FX 0 : AH - B 0F X 0 : A - BH 0AH W d1/2d2BH W d1/2d2the flatter the leaning anglethe larger the horizontal force the flatter the leaning angle, the larger the horizontal force in a way, this is a couple moment problem:AV and W @moment arm d1/2 vs B and AH @moment arm d25. equations of equilibrium5. equations of equilibriumtoday‘s objectivesroofs and bridges to show how to determinethe forces in the members ofa truss using the methods ofjoints to analyze the forces actingon the members of framesand machines composed ofpin-connected members6. structural analysis76.1 simple trusses

design assumptions all loadings are applied atthe joints, weight is typicallymuch smaller than externalloads and thus neglected all members are joinedtogether by smooth pins, thisimplies that each memberacts as a two-force membersimple truss threememberspinconnected at their ends forma rigid trianglerigidrigidtriangletriangle attachingtwomoremembers to form a newtriangle forms a larger truss a truss that is constructedby expanding a basic triangleis called a ‘simple truss’6.1 simple trusses6.1 simple trussesexample 6.1example 6.36.2 method of joints6.2 method of joints

identify zero-force members!pin-connected multi-force members frames and machines arecomposed of pin-connectedmulti-force members if only two members for atruss joint, and there are noother forces acting on it, thetwo members must be zeroforce members! frames are used to supportloads,machinescontainmoving parts to transmit andalter the effect of forces6.3 zero-force members6.6 frames and machinesexample 6.9example 6.96.6 frames and machines6.6 frames and machines14

example 6.9example 6.9for the frame shown below, draw a free body diagram of eachmember, the pin, and the two members together. calculate allforces! assume pin-type supports at the hands and feet.FHFHFVd1W1d1W2W1W2AHd2/4d2/4d2/4BHAV d2/4d2/4d2/4d2/4d2 B/4 V6.6 frames and machines6.6 frames and machinesexample 6.9example 6.9FHFHFVFHFHFHFVFHFVFVW2W1d1W1d1W2AHBHBHAV d2/4d2/4d2/4d2 B V/46.6 frames and machinesAHAVd2/4d2/4d2/4d2/4BV6.6 frames and machines

example 6.11example 6.116.6 frames and machines6.6 frames and machinesexample: structure with 3 subsystemsexample: structure with 3 subsystems6.6 frames and machines6.6 frames and machines

6.3 zero-force members identify zero-force members! if only two members for a truss joint, and there are no other forces acting on it, the two members must be zero force members! 6.6 frames and machines 14 frames and machines are composed of pin-connected multi-force members frames are used to support loads, machines contain

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