Strength of Materials

UNIT-01. SIMPLE STRESSES & STRAINS

Lecture Number - 04Prof. S.V. WANKHWDE

MECHANICAL DEPARTMENT SIT LONAVALA

Strength of Materials

Agenda

• Statically Indeterminate Members• Numerical.

Strength of Materials

Statically Indeterminate Members

• When the reactive forces or the internal resisting forces over a cross section exceed the number of independent equations of equilibrium, the structure is called statically indeterminate.

• These cases require the use of additional relations that depend on the elastic deformations in the members.

Strength of Materials

Problem 1: A steel bar shown in fig is having cross sectional area of

300 is held between two end supports and loaded by an axial forces of 30kN.

• Determine i)Reaction at A and B ii)Extension of left portion.

2mm

30 kNAR BR

0.3m 0.7m

A BC

Strength of Materials

30

30A B

B A

R R

R R

AR

0.3m

AR

0.7m

BR BR

0

0 0.3 (30 ) 0.7

21 & 9

AC BC

A B

A A

A B

L

RL RL

AE AE

R R

R kN R kN

A C

C B

Since both the ends A and B are rigidly fixed, there will be no deformation

0.105AR LL mmAE

Strength of Materials

• A steel circular bar PORS fixed rigidity at P and S. Bar is subjected to axial loads of 60kN and 120kN at Q and R as shown in Fig. Find the loads shared by each part of the bar and the displacement of the points Q & R. Take E for steel 207 2/kN mm

60kN 120kN

30mm

60mm

80mm

320mm 400mm 480mm

1

2

3

:

37.24

22.76

142.76

Ans

P kN

P kN

P kN

Problem 2

Strength of Materials

• A bar LMNP, fixed at L and P is subjected to axial forces at different location as shown in fig. Determine:

i) Forces in portion LM, MN, NPii) Displacement of points M and NTake E=200

Problem 3

2/GN m

50kN

0.5m 0.75m 1m

100kNR2

L MN P

21000mm

21500mm

22000mm

R1

1

2

3

:

66.67

16.67

83.33

0.167

0.208M

N

Ans

P kN

P kN

P kN

L mm

L

Strength of Materials

• A 40mm diameter bar is fixed at ends A and B. Two collar weighing 25kN and 40kN are placed at C and D resp. as shown in fig.

Find i)Reaction at ends A and B ii)stresses in each portion iii) Distance through which each collar movesAssume E=200Gpa

Problem 4

40kN

25kN

A

C

D

200mm

300mm

500mm:

40

25

56.59

21.22

35.37

A

B

AC

CD

DB

Ans

R kN

R kN

Mpa

Mpa

Mpa