Question

Determine the force in each member of the loaded truss. Make use of the symmetry of the truss and of the loading.

Answer 1

Calculate angles induced by truss members to find forces induced in members.

Calculate angle of the truss at point A by using the formula:

Here, 4 m is the height of the truss and 5 m is the width of truss at inclined member in truss.

Calculate force acting at point E by taking moments about point A:

Here, 30 kN force at point H, is acting at a distance of 5 m from point A, 60 kN force at point G, is acting at a distance of 10 m from point A, 30 kN force at point F, is acting at a distance of 15 m from point A and force at point E, is acting at a distance of 20 m from point A.

Write equation of equilibrium for the horizontal forces acting on the truss:

Here, is the reaction force acting on the truss at point A.

Write equation of equilibrium for the vertical forces acting on the truss:

Here, 30 kN is the force acting at point H, 60 kN is the force acting at point G, 30 kN is the force acting at point F and 60 kN is the reaction force acting at point E.

Calculate forces at point A by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint A:

Here, AB is the tension force acting in member AB.

Substitute, 60 kN for :

Here, negative sign indicates that the force AB is 96 kN compression.

Therefore, force acting in the truss member AB is .

Write equation of equilibrium for the horizontal forces acting at joint A:

Here, AH is the tension force acting in member AH.

Substitute, for AB:

Therefore, force acting in the truss member AH is .

Calculate forces at point B by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint B:

Here, BH is the tension force acting in member BH.

Substitute, 96 kN for AB:

Therefore, force acting in the truss member BH is .

Write equation of equilibrium for the horizontal forces acting at joint B:

Here, BC is the tension force acting in member BC.

Substitute, for AB:

Here, negative sign indicates that the force BC is 75 kN compression.

Therefore, force acting in the truss member BC is .

Calculate forces at point E by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint E:

Here, CH is the tension force acting in member CH.

Substitute, 60 kN for BH:

Here, negative sign indicates that the force CH is 48 kN compression.

Therefore, force acting in the truss member CH is .

Write equation of equilibrium for the horizontal forces acting at joint E:

Here, GH is tension acting in member GH.

Substitute, 75 kN for AH and for CH:

Therefore, force acting in the truss member GH is .

Calculate forces at point G by applying equations of equilibrium:

Write equation of equilibrium for the horizontal forces acting at joint G:

Here, FG is tension force acting in member FG.

Substitute, 112.5 kN for GH:

Therefore, force acting in the truss member FG is .

Write equation of equilibrium for the vertical forces acting at joint G:

Here, CG is tension force acting in member CG.

Therefore, force acting in the truss member CG is .

Calculate forces at point C by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint C:

Here, CF is the tension force in member CF.

Substitute, 48 kN for CH and 60 kN fr CG:

Here, negative sign indicates that the force CF is 48 kN compression.

Therefore, force acting in the truss member CF is .

Write equation of equilibrium for the horizontal forces acting at joint C:

Here, CD is the tension force in member CD.

Substitute, 48 kN for CH, 75 kN for BC and for CF:

Here, negative sign indicates that the force CD is 75 kN compression.

Therefore, force acting in the truss member CD is .

Calculate forces at point F by applying equations of equilibrium:

Write equation of equilibrium for the horizontal forces acting at joint F:

Here, EF is the tension in member EF.

Substitute, 48 kN for CF and 112.5 kN for FG:

Therefore, force acting in the truss member CD is .

Write equation of equilibrium for the vertical forces acting at joint F:

Here, DF is the tension in member DF.

Substitute, 48 kN for CF:

Therefore, force acting in the truss member DF is .

Calculate forces at point F by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint F:

Here, DE is the tension force in member DE:

Here, negative sign indicates that the force DE is 96 kN compression.

Therefore, force acting in the truss member DE is .

Answer 2

Calculate angles induced by truss members to find forces induced in members.

Calculate angle of the truss at point A by using the formula:

Here, 4 m is the height of the truss and 5 m is the width of truss at inclined member in truss.

Calculate force acting at point E by taking moments about point A:

Here, 30 kN force at point H, is acting at a distance of 5 m from point A, 60 kN force at point G, is acting at a distance of 10 m from point A, 30 kN force at point F, is acting at a distance of 15 m from point A and force at point E, is acting at a distance of 20 m from point A.

Write equation of equilibrium for the horizontal forces acting on the truss:

Here, is the reaction force acting on the truss at point A.

Write equation of equilibrium for the vertical forces acting on the truss:

Here, 30 kN is the force acting at point H, 60 kN is the force acting at point G, 30 kN is the force acting at point F and 60 kN is the reaction force acting at point E.

Calculate forces at point A by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint A:

Here, AB is the tension force acting in member AB.

Substitute, 60 kN for :

Here, negative sign indicates that the force AB is 96 kN compression.

Therefore, force acting in the truss member AB is .

Write equation of equilibrium for the horizontal forces acting at joint A:

Here, AH is the tension force acting in member AH.

Substitute, for AB:

Therefore, force acting in the truss member AH is .

Calculate forces at point B by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint B:

Here, BH is the tension force acting in member BH.

Substitute, 96 kN for AB:

Therefore, force acting in the truss member BH is .

Write equation of equilibrium for the horizontal forces acting at joint B:

Here, BC is the tension force acting in member BC.

Substitute, for AB:

Here, negative sign indicates that the force BC is 75 kN compression.

Therefore, force acting in the truss member BC is .

Calculate forces at point E by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint E:

Here, CH is the tension force acting in member CH.

Substitute, 60 kN for BH:

Here, negative sign indicates that the force CH is 48 kN compression.

Therefore, force acting in the truss member CH is .

Write equation of equilibrium for the horizontal forces acting at joint E:

Here, GH is tension acting in member GH.

Substitute, 75 kN for AH and for CH:

Therefore, force acting in the truss member GH is .

Calculate forces at point G by applying equations of equilibrium:

Write equation of equilibrium for the horizontal forces acting at joint G:

Here, FG is tension force acting in member FG.

Substitute, 112.5 kN for GH:

Therefore, force acting in the truss member FG is .

Write equation of equilibrium for the vertical forces acting at joint G:

Here, CG is tension force acting in member CG.

Therefore, force acting in the truss member CG is .

Calculate forces at point C by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint C:

Here, CF is the tension force in member CF.

Substitute, 48 kN for CH and 60 kN fr CG:

Here, negative sign indicates that the force CF is 48 kN compression.

Therefore, force acting in the truss member CF is .

Write equation of equilibrium for the horizontal forces acting at joint C:

Here, CD is the tension force in member CD.

Substitute, 48 kN for CH, 75 kN for BC and for CF:

Here, negative sign indicates that the force CD is 75 kN compression.

Therefore, force acting in the truss member CD is .

Calculate forces at point F by applying equations of equilibrium:

Write equation of equilibrium for the horizontal forces acting at joint F:

Here, EF is the tension in member EF.

Substitute, 48 kN for CF and 112.5 kN for FG:

Therefore, force acting in the truss member CD is .

Write equation of equilibrium for the vertical forces acting at joint F:

Here, DF is the tension in member DF.

Substitute, 48 kN for CF:

Therefore, force acting in the truss member DF is .

Calculate forces at point F by applying equations of equilibrium:

Write equation of equilibrium for the vertical forces acting at joint F:

Here, DE is the tension force in member DE:

Here, negative sign indicates that the force DE is 96 kN compression.

Therefore, force acting in the truss member DE is .