## Trusses- Problems

J A El-Rimawi (J.A.El-Rimawi@lboro.ac.uk) .

1. Calculate the degree of indeterminacy of the following pin jointed plane trusses, then determine whether each truss is stable. Start by identifying the triangulated (i.e. stiff/stable) parts of the structure and then examine how they are connected to each other and the supports.

1. What do you understand by the term compound truss? How stable/determinate is this pin-jointed truss? Calculate the reactions and the axial force in each member.
2.

(Answer: Reactions RB=250­ , RC=50­ ; Member forces: AD,DG=141.42(T); AB,BG =100(C); GH=100(T); BE,EH=212.13(C); HF,FC=70.71(C),BC=50(T); and zero.)

3. Analyse the truss shown qualitatively. Estimate the direction of the reactions, and deduce the sense of the axial force.
4.

5. Why is the truss shown statically determinate? Demonstrate this by hypothetical removal of members or reactions and in terms of equations v unknowns.
6. Calculate the reactions by careful choice of three equations of equilibrium and the equation of condition. Hence find the force in members BD and DC.

(Answer: VA= VG =75­ ; HA = - HG = 12.5® , FBD = 19.3 (T); FDC= 45.7 (C))

7. An elevation and plan of a space truss is shown opposite. Analyse the structure by computer (QSE) using a suitable combination of support conditions at B, C and D to make the structure statically determinate.

Check the vertical reactions by taking moments about the z-axis through B. All the horizontal reactions should be zero.

Check the forces in members AB, AC and AD by resolving at joint A along each axis; each equation should sum to zero. Express the force of each member along an axis as a ratio of its projected to actual length (the lengths of members AB, AC and AD are 7.07, 10.49 and 7.55 m).

(Answer: FAB = 6.4; FAC = 4.9; FAD = 4.2 (all C)).