The number of independent equations to be satisfied for static equilibrium of a plane structure is
For 2D plan 3 equastions for 3D space 6 equations
If there are m unknown member forces, r unknown reaction components and j number of joints, then the degree of static indeterminacy of a pin jointed plane frame is given by
Pin jointed plane frame Ds = m+r-2j Pin jointed space frame Ds = m+r-3j Rigid jointed plane frame Ds = 3m+r-3j Rigid jointed space frame Ds = 6m+r-6j
Number of unknown internal forces in each member of rigid jointed plane frame is
Degree of static indeterminancy of rigid jointed plane frame having 15 members, 3 reaction components and 14 joints is
For rigid join plan frame Ds = 3m+r-3j From given Ds = 3*15+3-3*14 Ds = 6
Degree of kinematic indeterminacy of a pin jointed plane frame is given by
Kinematic Indeterminacy for Pin jointed plane frame Dk = 2j-r Pin jointed space fram Dk = 3j-r Rigid jointed plane frame Dk = 3j-(r+m)+r' Rigid jointed space frame Dk = 6j-(r+m)+r'
Independent displacement components at each joint of a rigid jointed plane frame are
Fx, Fy, Mz Rotation Mz
If in a pin jointed plane frame (m+r)>2j, then the frame is
Ds = m+r-2j for stable is positive then indeterminate
A pin jointed plane frame is unstable if
If Ds negative then unstable
A rigid jointed plane frame is stable and statically determinate if
Which beam shown is unstable
1
Degree of kinematic indeterminacy of the beam shown is
1
Dk = 3j-(r+m)+r' Dk = 3*6-5*5+(2-1)+(2-1) Dk = 10
The rigid jointed frame shown is
1
Dk = 3m+r-3j Dk = 3*2+3-3*3 Dk = 0 Stable and determinate
The degree of kinematic indeterminacy of the pin jointed frame shown is
1
Dk = 2j-r Dk = 2*3-4 Dk = 2
The number of independent equestions to be satisfied for static equilibrium in a space structure is
For plane = 3 for space = 6
Degree of static indeterminacy of a pin jointed space frame is given by
The degree of static indeterminacy of a rigid-jointed space frame is
rigid jointed plane frame Ds = 3m + r – 3j space frame Ds = 6m + r - 6j
The degree of kinematic indeterminacy of a pinjointed space frame is
Kinematic indeterminacy Pin jointed plane frame 2j-r PIn jointed space frame 3j-r
The number of independent displacement components at each joint of a rigid-jointed space frame is
2d rigid joint = 3 3d rigid join = 6 2d truss joint = 2 3d truss joint = 3
If in a rigid-jointed space frame, (6m+r)<6j, then the frame is
Ds 0, Indeterminate and Stable