Assignment for IPE

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  ASSIGNMENT -1 ON ME 243 (IPE)Group- 1 : Roll 1108001~1108011 1. An angle bracket having thickness t = 0.5 in. is attached to the flange of a column by two 5/8-inch diameter  bolts see figure 1!. A uniformly distributed load acts on the to face of the bracket with a ressure  p = #00  si. $he to face of the bracket has length  L = % in. and width b = &.5 in. 'etermine the average bearing  ressure σ  b    between the angle bracket and the bolts and the average shear stress σ  aver   in the bolts. 'isregardfriction between the bracket and the column.!&. $he connection shown in the figure & consists of five steel lates( each #/1% in. thick( )oined by a single 1/*- in. diameter bolt. $he total load transferred between the lates is 1&00 lb( distributed among the lates asshown. a! +alculate the largest shear stress in the bolt( disregarding friction between the lates.b! +alculate the largest bearing stress acting against the bolt.   ,ig. for ue. o. 1 ,ig. for ue. o. & 3.   A cylindrical ressure vessel of length 1.& m and inner radius *00 mm is sub)ected to an internal ressure of 5 a. nowing that the thickness of the ressure vessel is at the ma2imum limit for a thin walled cylinder is to be considered( com ute the hoo stress and the elongation of the cylinder in its longitudinal direction due to the a lied ressure. $he material of the cylinder is steel. 4.   $he shaft shown in fig. * is securely fi2ed at A and is sub)ected to a tor3ue of 8 k.m. 4f ortion A is asolid shaft of 100 mm diameter and ortion + is hollow( with e2ternal diameter 100 mm and internaldiameter 65 mm( find the ma2imum shear stress develo ed in the shaft. Also find the values of ma2imumangle of twist. $ake 7 = 80 k/m & . ,ig. for ue. o. *,ig. for ue. o. 55.   A rigid bar of negligible weight is su orted as shown in ,ig. 5. 4f  = 80 k( and the rods are sub)ected to tem erature change of #0 0 +( determine the stress in and energy absorbed by the steel rod. Assume the coefficients of linear e2 ansion are 11.6 9m/m:;+! for steel and 18.< 9m / m:;+! for brone.%. 'raw the shear force and bending moment diagram for the beam loaded as shown in the fig. %.   ,ig. for ue. o. % ASSIGNMENT -1 ON ME 243 (IPE)Group- 1 : Roll 1108012~1108022 1. A uniform bar  AB of weight W = &5  is su orted by two s rings( as shown in the figure 1. $he s ring on the left has stiffness k  1 = #00 /m and natural length  L 1  = &50 mm. $he corres onding 3uantities for the s ring on the right are k  &  = *00 /m and  L &  =&00 mm. $he distance between the s rings is  L = #50 mm( and the s ring on the right is sus ended from a su ort that isdistance h = 80 mm below the oint of su ort for the s ring on the left. At what distance  x from the left-hand s ring should aload  P = 18  be laced in order to bring the bar to a horiontal osition>&. 4n the steel structure shown &( a 8 mm diameter in is used at A and 1&-mm-diameter ins are used at  and '. $he ultimate shearing stress is 100 a at all connections and the ultimate normal stress is &50 a in ?ach of the two links )oining  and '( determine the allowable load ( if an overall factor of safety of #.0 is desired.  ,ig. for ue. o. 1 ,ig. for ue. o. & #.   A cylindrical ressure vessel is fabricated from steel lating that has a thickness of &0 mm. $he diameter of the  ressure vessel is *50 mm and its length is &.0 m. 'etermine the ma2imum internal ressure that can be a lied if the longitudinal stress is limited to 1*0 a( and the circumferential stress is limited to %0 a.*.   A stiff bar of negligible weight transmits a load  to a combination of three s rings as shown in fig. $he s rings aremade u of the same material and out of wire of e3ual diameter. $hey are of the same length before loading. $henumber of coils in the three s rings are 10( 1&( and 15 res ectively( hile the mean radii are in the ratio of 1@ 1.& @1.* res ectively. ,ind the distance 2 such that the bar remains horiontal after a lying the load.  ,ig. for ue. o. *,ig. for ue. o. 5 5. A steel bar( 1 m in length and #5 2 #5 mm in cross-section( is rigidly attached to a wall at its right ends. 4ts other endis 0.5 mm from another rigid wall. 4f a 1&0-k a2ial force is attached to the bar at its mid oint and its tem erature isincreased %0 0 +( a! what will be the unit stress in each ortion of the bar> b! hat will be the unit stress in each  ortion of the bar if the wall A is removed other condition remains the same!> ? = &06 7/m & (  = 0.0000116/ 0 +.%. 'raw the shear force and bending moment diagram for the beam loaded as shown in the figure %. eglect the weightof the beam.   ,ig. for ue. o. % ASSIGNMENT -1 ON ME 243 (IPE)Group- 3 : Roll 1108023~1108031, 1008030, 0808030 1. +om ute the energy re3uired by the driver for the system shown in fig 1. $he load  a lied by the driver is 100 lb. A+ is a rigid bar and + is a wire whose total length is *0 in( diameter 0.08 in( and its materialBs modules of elasticity is 1& 2 10 %   si.  ,ig. for ue. o. 1 ,ig. for ue. o. & &. $hree wires connect two rings as shown in the figure. $heir characteristics are as follows@ 'etermine the tensile unit stress and the final length of wire CaD after a load of  = 1.5 k is a lied at the lower ring.#. A cylindrical steel ressure vessel *00 mm in diameter with a wall thickness of &0 mm( is sub)ected to an internal  ressure of *.5 /m&. a! +alculate the tangential and longitudinal stresses in the steel. b! $o what value may theinternal ressure be increased if the stress in the steel is limited to 1&0 /m&> c! 4f the internal ressure wereincreased until the vessel burst( sketch the ty e of fracture that would occur.*. A com ound shaft consisting of a steel segment and an aluminum segment is acted u on by two tor3ues as shown in ,ig. *. 'etermine the ma2imum ermissible value of $ sub)ect to the following conditions@ E st  F 8# a( E al  F 55 a( and the angle of rotation of the free end is limited to %;. ,or steel( 7 = 8# 7a and for aluminum( 7 = &8 7a.  ,ig. for ue. o. * ,ig. for ue. o. 5 5. A com osite round bar made u of aluminum and steel is held between two su orts as shown in the fig. $he barsare stress free at a tem erature of *0 0 +. hat will be the stresses in the two bars when the tem erature is &0 0 +( if the  su orts come nearer to each other by 0.1 mm. 4t can be assumed that the change of tem erature is uniform all alongof the length of the bar@ $ake? st  = &10 7/m & ( ? al  = 6* 7/m & (  st  = 11.6 2 10 -%   er 0 +(  al  = &#.* 2 10 -%   er 0 +( %. 'raw the shear force and bending moment diagram for the beam loaded as shown in the figure. eglect the weight of  the beam.  ,ig. for ue. o. %
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