Draw the Sfd Bmd

8/9/2019 Draw the Sfd Bmd

1/12

SHEAR FORCE AND BENDING MOMENT DIAGRAMS

QNo 1. Draw the shear force and bending moment diagram for the beam asshown in g

QNo 2 Draw the shear force and bending moment diagram for the beam as shownin g

QNo 3. Draw the shear force and bending moment diagram for the beam asshown in g

QNo 4. Draw the S.F. and B.M. diagrams for the beam loaded as shown in Fig.,and determine (a) the position and magnitude of the maximum B.M., and (b) theposition of any point of contraexure.

QNo5. Draw the shear force and bending moment diagram for the beam as shownin g


2/12

QNo6. A beam ABCDE is simply supported at A and D. t carries the followingloading! a distributed load of "# $%&m between ' and a concentrated load of #$% at B; a concentrated load of # $% at *+ a concentrated load of # $% atE; adistributed load of -# $%&m between D and E. Span AB ./ m, * CD DE m. *alculate the 0alue of the reactions at A and D and hence draw the S.F. andB.M. diagrams. 1hat are the magnitude and position of the maximum B.M. on thebeam2Ans: [41.1, 113.9kN; 28.15kNm; 1.37m from A.]QNo7. ' beam '*D, - m long, is simply3supported at the right3hand end D and

at a point B lm from the lefthand end A. t carries a 0ertical load of # $% at A, asecond concentrated load of # $% at *, " m from D, and a uniformly distributedload of # $%&m between C and D. Determine!!" the 0alues of the reactions at and D,(b) the position and magnitude of the maximum bending moment. Ans : #33 $N, 27 $N, 2.7 m %&om D, 36.45 $ Nm.'QNo(. Dene a beam. 1hat is a cantile0er, a simply supported and a o0erhungbeam2 1hat is the point of contraexure 2 Draw the shear force and bendingmoment diagram for the beam as shown in g

QNo). Determine the maximum shearing force and bending moment in the simplysupported beam shown in Fig. -3". Ans. / "4" %, 4456 % m

QNo1*. Draw the shear force and bending moment diagram for the beam as

shown in g


3/12

+RE BENDING OF BEAM

QNo1. ' uniform 73section beam is ## mm wide and /# mm deep with a angethic$ness of / mm and a web thic$ness of mm. f the limiting bending stressesfor the material of the beam are 4# 8%&m in compression and -# 8%&m intension, nd the maximum u.d.. that the beam can carry o0er a simply supportedspan of 5 m.

QNo2. ' simply supported rectangular beam with symmetrical section ##mm indepth has moment of inertia of .- x #3/ m9 about its neutral axis. Determine thelongest span o0er which the beam would carry a uniformly distributed load of 9:%&m run such that the stress due to bending does not exceed / 8%&m.

QNo3. ' rectangular beam of ## mm in width and 9## mm in depth is simplysupported o0er a span of 9m and carries a distributed load of # :%&m. Determine

maximum bending stress in the beam.

QNo4. ' wooden beam of rectangular cross section is sub;ected to a bendingmoment of /:%m. f the depth of the section is to be twice the breadth and stressin wood is not to exceed -#%&cm. Find the dimension of the cross section of thebeam.

QNo5. ' beam ha0ing I < section is shown in g is sub;ected to a bending momentof /## %m at its %eutral axis. Find maximum stress induced in the beam.

QNo6. ' cast iron brac$et sub;ected to bending has cross section of I < form withune=ual anges. f maximum ending moment on the section is 9# 8%3mm,determine 8aximum bending stress. 1hat should be the nature of stress2


4/12


5/12

(a) 7he outside diameter of brass tube.(b) 8aximum shear stress induced in steel and brass.

STRESS AND STRAIN

QNo1. ' circular rod of diameter # m and /## m long is sub;ected to tensile forceof 9/$%. 7he modulus of elasticity for steel may be ta$en as ## $%&m. Findstress, strain and elongation of bar due to applied load.

QNo2. ' rod ## cm long and of cm x cm cross3section is sub;ected to a pull of ### $g force. f the modulus of elasticity of the materials .# x #- $g&cm,

determine the elongation of the rod.

QNo3. ' hollow cast3iron cylinder 9 m long, "## mm outer diameter, andthic$ness of metal /# mm is sub;ected to a central load on the top when standingstraight. 7he stress produced is 6/### $%&m. 'ssume BoungCs modulus for castiron as ./ x #4 :%&m nd(i) magnitude of the load,(ii) longitudinal strain produced and(iii) total decrease in length.

QNo4. 7he following data was recorded during tensile test made on a standardtensile test specimen!riginal diameter and gauge length / mm and 4# mm+8inimum diameter at fracture / mm+Distance between gauge points at fracture 5/ mm+Eoad at yield point and at fracture /# $% and -/ $%+8aximum load that specimen could ta$e 4- $%.8a$e calculations for(a) Bield strength, ultimate tensile strength and brea$ing strength(b) Aercentage elongation and percentage reduction in area after fracture(c) %ominal and true stress and fracture.

QNo5. ' steel bar is 5## mm long+ its two ends are 9# mm and "# mm in diameterand the length of each rod is ## mm. 7he middle portion of the bar is / mm in


6/12

diameter and /## mm long. f the bar is sub;ected to an axial tensile load of / $%,nd its total extension. 7a$e E ## @%& m .

QNo6. ' member ABCD is sub;ected to point loads A, A, A" and A9 as shown in Fig.*alculate the force P",necessary for e=uilibrium if P # kN, P # kN and P9 -# kN.Determine also the net change in length of the member. 7a$e E ## @%&m.

QNo7. 7he bar shown in Fig. is sub;ected to an axial pull of /#$%. Determinediameter of the middle portion if stress there is limited to /%&mm. Aroceed todetermine the length of this middle portion if total extension of the bar is speciedas #./ mm. 7a$e modulus of elasticity of bar material E #/ %&mm.

QNo(. ' rod ABCD rigidly xed at the ends A and D is sub;ected to two e=ual andopposite forces P / kN at B and C as shown in the g gi0en below! 8a$ecalculations for the axial stresses in each section of the rod.

QNo). ' s=uare bar of / mm side is held between two rigid plates and loaded byan axial pull e=ual to "##$% as shown in Fig.. Determine the reactions at end A andC and elongation of the portion AB. 7a$e E #/ N&mm.

QNo1*. ' steel bar is sub;ected to loads as shown in g. . Determine the changein length of the bar ABCD of 4 cm diameter. E 4# kN&mm.


7/12

QNo11. For the bar shown in Fig. 9.", calculate the reaction produced by thelower support on the bar. 7a$e E ## GN&m. Find also the stresses in the bars.

QNo12. ' 6## mm length of aluminium alloy bar is suspended from the ceiling soas to pro0ide a clearance of #." mm between it and a /# mm length of steel baras shown in Fig. 9.". 'al /# mm, Gal 6# GN&m

, 's /## mm, Es #GN&m. Determine the stress in the aluminium and in the steel due to a "##kN loadapplied /## mm from the ceiling.

QNo13. 7wo copper rods one steel rod lie in a 0ertical plane and together supporta load of /#$% as shown in Fig. . Gach rod is / mm in diameter, length of steelrod is " m and length of each copper rod is m. f modulus of elasticity of steel istwice that of copper, ma$e calculations for the stress induced in each rod. t maybe presumed that each rod deforms by the same amount.


8/12

QNo14. ' beam weighing /# % is held in horiHontal position by three wires. 7heouter wires are of brass of .4 mm dia and attached to each end of the beam. 7hecentral wire is of steel of #.5 mm diameter and attached to the middle of thebeam. 7he beam is rigid and the wires are of the same length and unstressedbefore the beam is attached. Determine the stress induced in each of the wire. 7a$e BoungCs modulus for brass as 4# GN&m and for steel as ## GN&m.

QNo15. ' steel rod # mm diameter passes centrally through a steel tube / mminternal diameter and 9# mm external diameter. 7he tube is 6/# mm long and isclosed by rigid washers of negligible thic$ness which are fastened by nutsthreaded on the rod. 7he nuts are tightened until the compressi0e load on the tubeis #$%. *alculate the stresses in the tube and the rod. Find the increase in thesestresses when one nut is tightened by one =uarter of a turn relati0e to the other. 7here are #.9 threads per mm length. 7a$e E ## @%&m.QNo16. 7wo parallel walls - m apart, are stayed together by a steel rod # mmdiameter, passing through metal plates and nuts at each end. 7he nuts are

tightened, when the rod is at a temperature of ##I*. Determine the stress in therod, when the temperature falls down to #I*, if () 7he ends do not yield.() 7he ends yield by mm. 7a$e G .# #/%&mm, as #


9/12

THERMA- STRESSES

QNo1(. ' steam pipe is "# m long at a temperature of /K*. Steam at 4#I* ispassed through the pipe. *alculate the increase in length when the pipe is free toexpand. 1hat stress is induced in the material if the expansion is pre0ented 2

(E ## @%&m, J #.#### per I*)

QNo1). ' steel rod ./ m long is secured between two walls. f the load on the rodis Hero at #I*, compute the stress when the temperature drops to 3#I*. 7hecross3sectional area of the rod is ## mm, J .6 Lm&(mI*), and G ##@Aa,assuming(a) that the walls are rigid and(b) that the walls spring together a total distance of #./ mm as the temperaturedrops.

QNo2*. ' circular bar of length 9## mm and tapering uniformly from /# mm to /mm diameter is held between rigid supports at the ends. *alculate the maximumand minimum stress de0eloped in the bar when the temperature is raised by "#I*. 7a$e E #/ %&mm and J . #


10/12


11/12

compressi0e respecti0ely. Gstimate the shear stress to which material could besub;ected, if the maximum principal stress is /# 8%&m. 'lso nd the magnitudeof other principal stress and its inclination to # 8%&m.

QNo2. ' load carrying member is sub;ected to the following stress condition+ 7ensile stress J x 9##8Aa+ 7ensile stress J y < "##8Aa+

Shear stress τ xy ##8Aa (*loc$ wise)+btain() Arincipal stresses and their plane() 8aximum shearing stress and its plane

QNo3. 7he state of stress at a point in a loaded component principal stresses is

found to be as gi0en below ! J x /# @%&m+ J y /# @%&m+ τ xy ##@%&m+Determine the principal stresses and maximum shearing stress. Find theorientations of the planes on which they act

QNo4. ' plane element is sub;ected to following stresses J x #:%&m

(tensile),J y 9# :%&m (*ompressi0e) and τ xy /#:%&m (counter cloc$wise on the plane

perpendicular to x 3axis)nd() Arinciple stress and their direction() 8aximum shearing stress and its directions.(") 'lso, nd the resultant stress on a plane inclined 9## with the x 3axis.

QNo5. 't a point in a stressed body, the principal stresses are J x 4# $%&m

(tensile) and J y 9# $%&m (*ompressi0e). Determine normal and tangentialstresses on planes whose normal are at "#I arid #I with x 3axis using 8ohrMs

stress circle 8ethod.

QNo6. 7he strain measured on a strain rosette are as follows

ε#o9/##3- , ε-## 3-###3- , ε##/##3-

Determine the stresses and their directions G##@Aa and AoissonMs ratioo."

A s//0 !& o% so0 &0!& &osss/on s 5* mm n !m//&. T/ !& s8nn/ ! o /ns !n s9// o !!0 om8&/sson. I% / 0m o% 8&o8o&on!0; o% / m!/&!0 s 21* M+! !n E < 2** G+!, //&mn/ / mmnmm 0/n= o > E0/&?s %o&m0! s @!0. A0so //&mn/ / @!0/o% E0/&?s $0n= 0o! % / o0mn !s s mnmm 0/n=.

Tn C;0n/& !n +&n8!0 S&/ss

. ' boiler is sub;ected to an internal steam pressure of %&mm. 7he thic$ness of boiler plate is .# cm and permissible tensile stress is # %&mm. Find out themaximum diameter, when eNciency of longitudinal ;oint is 5#? and circumference

;oint is 9#?. . ' cylindrical shell is ./ m diameter and 9 m long closed at both ends is sub;ectedinternal pressure of " %&mm. 8aximum circumferential stress is not to exceed /#%&mm. Find changes in diameter, length, and 0olume of the cylinder. G x # /

%&mm, AoissonOs ratio #./. ". ' cylinder has an internal diameter of "# mm, wall thic$ness / mm and is mlong. t is found to change in internal 0olume by x # 3- m" when lled with a li=uid


12/12

at a pressure PpO. 7a$ing G ## @Aa and AoissonOs ratio #./, determine thestresses in the cylinder, the changes in its length and internal diameter.9. ' cast iron pipe of "## mm internal diameter and mm thic$ is wound closely witha single layer of circular steel wire of / mm diameter under a tension of -# 8Aa. Findthe initial compressi0e stress in the pipe section. 'lso nd the stresses set up in thepipe and steel wire, when water under a pressure of 9 8Aa is admitted into the pipe.

7a$e G for cast iron and steel as ## @Aa and ## @Aa respecti0ely. AoissonOs ratio

#."./. ' steel cylinder with at ends is m long and m diameter with metal thic$ness #mm. t is led with water at atmospheric pressure. 7he pressure has been increased to8Aa by pumping more water. 'n amount of .5 x #- mm" of water has beencollected at the outlet after releasing the pressure. f E x #/ 8Aa and poisonOsratio #.", nd out the bul$ modulus.-. ' boiler drum consists of a cylindrical portion 9 m long,./m in diameter and./mm thic$. ts closed by hemispherical ends.n hydraulic test to - 8%&m,how muchaddional water will be pumped in after initial lling at atmospheric pressure2G##@%&m : water ." @%&m and &m#."

Documents

Draw the Sfd Bmd