PROBLEMS

5.41 Using tbe method of Sec. 5.3 , solve Prob. 5. 1.

5.42 Using th巴 Ill ethod of Sec. 5.3, so l v巴 Prob.5 .2

5 .43 Using the method of Sec. 5.3, solve Prob. 5.3.

5 .44 Using the 111巴thod of Sec. 5 .3, solve Prob. 5 .4

5.45 Using the Illethod of Sec. 5.3 , solve Prob. 5.5

5 .46 Using the 1ll巴的od of Sec. 5.3 , solve Prob. 5.6

5.47 Using th巴 Ill ethod of Sec. 5.3 , solve Prob. 5. 13.

5.48 Using the me thod of Sec. 5.3 , solve Prob. 5. 14

5.49 Us ing the ll1ethod of Sec. 5.3, so lve Prob. 5 .15.

5.50 Using th巴 ll1ethod of Sec. 5 .3, solve Prob. 5. 16.

5.51 and 5.52 Draw th巴 sbear ancl b巴ncling- 1lloment diagra ll1s for the bea m and loading shown , anχ吋CI CI 巴訓t巴白1111t叫h巴 sh巴a r， (b) of the bending IllOll1ent.

240111111 240111111 240111111

1- ~I- ; 1- -1 「L B

120 N l20 N

Fig. P5.51 Fig. P5.52

5.53 Using the ll1ethod of Sec. 5.3 , so lve Prob. 5 .2 1.

5.54 Using the ll1ethod of Sec. 5.3 , so lve Prob. 5 .22.

5.55 Using the ll1ethocl of Sec. 5 .3, solve Prob. 5.23.

5.56 Using the method of Sec. 5.3 , solve Prob. 5.24.

328

5.57 and 5.58 Determine (a ) the equations of th巴 shea r and b巴ndingmoment curves for the given beam and loading, (b ) the max imu l11 absolute value of th巴 bending 1l10ment in th巴 bea ll1

Problems 329

ω = 叫。 (1 一 i )lV 7T X

t υ = ωυ$111 τ

β

Fig. P5.57 Fig . P5.58

5.59 Determine (a) the equation s of the shear and bending- ll1oment c lI rves for the given bea ll1 and loading , (b) tb巴 m扎ximu ll1 abso lut巴 valu巴 of th巴

bending 11l0 l1lent in the bea l1l

B

u

u

t

I

Fig. P5.59 Fig. P5.60

5.60 For the beam and loading shown , determine the eqllations of the shear and bending- l1lo l1le nt c lIrves and the ll1axil1l u l1l abso l ut巴 va l lle of the b巴nding moment in the bea l1l , knowing that (a) k = 1, (b) k = 0.5

5.61 and 5.62 Draw the shear and b巳nding- l1lo l1lent di agra l1ls for th巴bea l1l and loading shown and deterl1l in巴 tbe maXi l1l ll ll1 norm al stress due to bending .

9kN

A

16 kN/1ll

T出

1-1 1-- 一一一一一三一一IB 11

LMm- LYJIM W200 x 19.3

Fig. P5.61 Fig. P5.62

330 Analysis and Design 01 Beams lor Bending 5.63 and 5.64 Draw the shear and bending- ll1omenl diagrallls for lhe bealll and loacl ing shown ancl c1 elerll1 ine the lllaXilllU Il1 nor ll1al slress c1 ue to bencling

45 kN/1ll •

l ttttttttt c 1 6 、 l l1〔寸A 戶三三三三三三三三主三三~ BJ 仆 1250 Ill lll -A ~ U i.

|-um-LJ此

ltttttt c l r-o

AI 一「 一了 113 II

L ln-L18 111EL

28 kN

Fig. P5.64

5.65 and 5.66 Draw the shear ancl bencling-Illomenl c1 iagrallls for lhe bealll ancl loacl ing shown ancl CI巴 l erll1 in e lh巴 Ill ax imum nor ll1al slress c1 u巴 10bencling

10 kN

~

B 日1ttttttttt| 干干寸

I C f \ 76 111111

L川IJHiFig. P5.65

Fig. P5.66

5.67 and 5.68 Draw the shear and b巴ncling白 1l10 1ll巴 nt c1 iagrams I'or lh巴b巴a lll ancl loacling shown ancl c1 eterll1 ine the maxl mulll norll1日 I slress c1 u巴 10bencling

2kN

cl 0 l 13

t'm1-，士 IllJz \]

… z

W410 x 114

Fig. P5.68

331 Problems 5.69 Beam AB , 0 1' 1巳ngth L and sqll a re cross section of side a, is Sllp­ported by a piVOl at C and loaded as shown. (a) Check lhal the beam is in eqll 卜librilllll. (b) Show that the maximllm normal S tl 巴ss du巴 to b巴nding OCCllrs at C and is eq叫 to ?Uι2/( 1.5at

門

υ (n.~λ L v t的

0.36111一~O.36 1ll一|

也可

什

5.70 Knowing that rod AB is in equilibrillm llnder the loadin g shown , draw th巴 shea r and bending- moment diagrams and d巴l巴rllline th巴 maximllm

nor l11al stress dlle to bending

18 Ill lll 1-1

日 311111

P *5.71 Beam AB sllpports a unifor ll1 ly distribllted load of 1 5 肘-l/m and two concenlraled loads P and Q. It has been experimentall y de le rmined that the normal slress dll巴 to bend ing on the botto ll1 edge of the beam is -56.9 MPa at A and -29.9 MPa a l C. Draw the shear and bendin g- moment diagra ll1s fOl

the beam and de te rmine the magnitudes of the loads P and Q.

*5.72 Beam AB SllppOrtS a llllÍ for ll11y di stribllted load of 15 kN/m and lwo concentrated loads P and Q. Il has been 巴xp巴rimenta lJ y dele rmined th at lhe nor ll1al stress dlle to bending on th巴 bottom edg巴 of th巴 l ow巴r flange of the W250 X 32.7 rolled-sleel beam is + 14 MPa al D and + 5.35 MPa al E. (a) Draw the shear and bending- moment diagrams for the beam. (b) Determine the maximllm normal stress dlle to bend ing that OCCllrs in the beam.

z 心Z

Q

R-

1; 1: 1[ '，，『ll

」'-

-

-

N

T4土

,: li w

b「IL-

-

l

汁叫一一

F

Fig. P5.73

*5.73 Beam AB sllpports a llniforml y di stribllted load of 8 kN/ m and two concenlrated loads P and Q. lt has been ex p巴rimentally de te rmined th at the normal s t! 巴ss dlle 10 b巴nding on the bottom edge of th巳 lower flange of the W200 X 52 rolled-s tee l bea m is 100 MPa at D and 70 MPa al E. (a) Draw the shear and b巴ncling-moment diagrams for the beam. (b) Determine the max­imum n01111a l stress dlle to bendin!! tha t occurs in th巴 beam.b