工程力学练习册答案(下)4-

材料力学习题解答弯曲内力P73

40-1(a)FABCqFABCqFS1M1112233FS1=q×2-

F=10kNFCFBCM1=F×4-2q×1=20kN·mFS2M2FS3M3FS2=-

F=-10kNM2=F×2=20kN·mFS3=FS2=-10kNM3=M2=20kN·mFS1+

F-q×2=0Fy

=0

F×4

-

M1

-

2q×1=0mA

=0

求指定截面的内力

截面法!(难?)

相邻截面(正负号规定)

P73

40-1(b)3qABCAA3qAB3qCFAFCFAFAFAFCFS2M2FS3M3FS1M1FS3M3112233FA

=

40kNFC

=

80kNmA

=0

Fy

=0

FS1=FA=40kNM1=0FS2=FA=40kNM2=FA×2=80kN·mFS3=FA

-3q×2=-20kNM3=FA×4-3q×2×1=100kN·m特殊位置截面P73

40-1(c)FAFBABCFFAACFCFFS1M1FS2M2FS3M3112233a

=l

FA

=

5kNFB

=

15kNmA

=0

Fy

=0

FS1=-

FA=-5kNM1=-

FA×2=-10kN·mFS2=F=10kNM2=-

F×1=-10kN·mFS3=F=10kNM3=0相邻截面P73

40-1(d)FDMO(3Fa)ACDBFAFFDCDFDCDFS1M1FS2M2FS3M3112233a

=l

FD

=

10kNFy

=0

FS1=-

F=-10kNM1=-

F×1=-10kN·mFS2=-

FD=-10kNM2=FD×2=20kN·mFS3=-

FD=-10kNM3=FD×1=10kN·m相邻截面P73

40-1(e)FCABCDFEFEFAFBABFCFAAFAFBABDFEFE112233FC

=

5kNFE

=

5kNmC

=0

Fy

=0

FB

=

7.5kNFA

=

2.5kNmB

=0

Fy

=0

FS1M1FS1=-

FA=-2.5kNM1=-

FA×1=-2.5kN·mFS2M2FS2=FB

-

FA=5kNM2=FB×1-

FA×3=0FS3M3FS3=F

-

FE=5kNM3=FE×3-

F×1.5=0特殊位置截面相邻截面多跨梁

(有主次之分)

P74

40-2-1FABC2FF2F2Fa3FaxxAB段:

BC段:

=-

FM(x)

=2F×(2a-x)

-

F×(a-x)

=3Fa

-

FxFS(x)

=F-2FxM(x)

=2F×(2a-x)

=4Fa

-2FxFS(x)

=

-2FM

图FS图按比例

建立坐标

M图

正确性

差

P74

40-2-2ABCqqa32qa212qa2xAB段:

BC段:

xM(x)

=-

qa×(2a-

a-x)

=qax

-

qa2FS(x)

=qaM(x)

=q×(2a-x)×(2a-x)

=-

qx2+2qax-2qa2FS(x)

=q×(2a-x)

2

3

2

1=2qa

-

qx

2

1

2

1

2

1=-

q×(2a-x)2M

图FS图x光滑

P74

40-2-3FAFBABCFFD13F13F23F13Fa13FaxFA

=

FFB

=

FmA

=0

Fy

=0

3

1

3

1AC段:

DB段:

CD段:

xxx=FM(x)

=FA×x

=FxFS(x)

=FAM(x)

=FAx-

F×(x-a)

=

Fa-

FxFS(x)

=FA-F

=-

F

3

1

3

1

3

2

3

2=FFS(x)

=FB

3

1

3

1M(x)

=-FB×(3a-x)

=

Fx-

FaM

图FS图P74

40-2-4FAFCABCFDM0(Fa)FFaFFaFA

=

FFC

=2FmA

=0

Fy

=0

xxxxAB段:

CD段:

BC段:

=-FM(x)

=-FA×x

=-FxFS(x)

=-FAM(x)

=-FA×x+M0

=

Fa-

FxFS(x)

=

-FA

=-FFS(x)

=FM(x)

=-F×(3a-x)

=

Fx-3FaM

图FS图P75

41-1-1ABCqqqa2qa12qa218qa212qa218qa2形状:

FS图M

图斜直线

斜直线

FSA

=0FSB

=qaFSC

=0FSB

=qaMA

=0MD

=qa2

8

1MB左

=qa2

2

1MB右

=-

qa2

2

1ME

=-

qa2

8

1MC

=0DE形状:

抛物线

抛物线

简便方法微分关系(突变)(特殊点)(形状.方向)P75

41-1-2FBFCABqaCqqaqa24972qa2116qa76qaDFS图形状:

水平线

斜直线

FSB左

=-

qaFB

=

qaFC

=

qamB

=0

Fy

=0

6

17

6

7FSB右

=qa

6

11FSC

=-

qa

6

7M

图形状:

斜直线

抛物线

MA

=0MD

=qa2MB

=-

qa2MC

=0MB

=-

qa2

72

49a

6

7(突变)(特殊点)P75

41-1-3FAFDADBqaCq34qa14qa54qa98qa234qa2FD

=

qaFA

=

qamD

=0

Fy

=0

4

3

4

5FS图形状:

水平线

水平线

斜直线

FSB左

=qaFSB右

=-

qaFSC

=-

qaFSD

=-

qa

4

3

4

1

4

1

4

5MA

=0MC

=qa2MB

=qa2MD

=0MB

=qa2M

图形状:

斜直线

斜直线

抛物线

MC

=qa2ME

=qa2

8

9

8

9

4

3

4

3

2

112qa2E(突变)(按比例)P78

42-2-1ABCFFaABCM0(Fa)ABCFM0(Fa)F2FaFa2Fa3FaFaaM

图(M0)M

图M

图(F)FS图(M0)FS图FS图(F)叠加法(过程)P78

42-2-2AC