UNIT-01. SIMPLE STRESSES & STRAINS Lecture Number - 04 Prof. 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

Determine i)Reaction at A and B ii)Extension of left portion. 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. A C B 30 kN 0.3m 0.7m Strength of Materials

A C C B 0.3m 0.7m Since both the ends A and B are rigidly fixed, there will be no deformation Strength of Materials

Problem 2 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 30mm 60 mm 120kN 80mm 60kN 320mm 400mm 480mm Strength of Materials

Forces in portion LM, MN, NP Displacement of points M and N Take E=200 Problem 3 A bar LMNP, fixed at L and P is subjected to axial forces at different location as shown in fig. Determine: Forces in portion LM, MN, NP Displacement of points M and N Take E=200 N P M L R2 R1 50kN 100kN 0.5m 0.75m 1m Strength of Materials

Find i)Reaction at ends A and B ii)stresses in each portion Problem 4 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 moves Assume E=200Gpa A 200mm C 300mm 25kN D 500mm 40kN Strength of Materials