Pin jointed Frames

Pin jointed frames, generally, transfer the applied loads by inducing axial tensile or compressive forces in the individual members. The magnitude and sense of these forces can be determined by using standard methods of analysis.

The following tutorial questions require that the forces in the individual elements be solved by either the "method of sections" or the "method of joints".

The "method of sections" involves the application of the three equations of static equilibrium to a two dimensional plane frame. An imaginary section line cuts the frame in two. Since there are only three equations of equilibrium, the section through the frame must not include any more than three members for which the internal forces are unknown.

The "method of joints" considers the isolation of each individual joint. For each joint, as the forces are coincident the moment equation is of no value leaving only two equations of equilibrium available to resolve the forces in the members. The equilibrium of each joint must be considered in a sequence that ensures that there are no more than two unknown member forces in each joint under consideration.

Notes:

  • The analysis associated with these tutorial questions will round all your input values as follows:
    • Forces, e.g. vertical and horizontal reactions (kN) - 1 decimal place.
    • Dimensions (m) - 3 decimal places.
    • Angles (°) - 1 decimal place.
  • Numeric answers are required in all the fields. If you calculate a force as being zero, enter zero (0) in the appropriate field.
  • You are only able to print the current question as a tutorial question if you have not submitted your answers.
  • Once a tutorial question has been printed, you will not be able to submit your answers, or see the solution to that particular question.
Tutorial 1 - Pin Jointed Frame

For the simply supported pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & C.
  • The magnitude of the internal forces for all the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ C - Hc = kN

Vertical Reactions

@ A - Va = kN
@ C - Vc = kN

Member Forces

MAB= kN
MAD= kN
MBC= kN
MCD= kN
MBD= kN
Tutorial 2 - Pin Jointed Frame

For the simply supported truss, calculate the following:

  • The horizontal and vertical reactions at the supports A & E.
  • The magnitude of the internal forces for all the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive values for a member force indicates a tie, i.e. a tension member.
  • A negative values for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ E - He = kN

Vertical Reactions

@ A - Va = kN
@ E - Ve = kN

Member Forces

kN
kN
kN
kN
Tutorial 3 - Pin Jointed Frame

For the simply supported pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & L.
  • The magnitude of the internal forces for the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ L - Hl = kN

Vertical Reactions

@ A - Va = kN
@ L - Vl = kN

Member Forces

kN
kN
kN
kN
Tutorial 4 - Pin Jointed Frame

For the simply supported pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & E.
  • The magnitude of the internal forces for all the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ E - He = kN

Vertical Reactions

@ A - Va = kN
@ E - Ve = kN

Member Forces

kN
kN
kN
kN
Tutorial 5 - Pin Jointed Frame

For the pin jointed frame, calculate the following:

  • The inclined reaction at support D.
  • The horizontal and vertical reactions at the supports D & B.
  • The magnitude of the internal forces for all the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive values for a member force indicates a tie, i.e. a tension member.
  • A negative values for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ D - Hd = kN
@ B - Hb = kN

Vertical Reactions

@ D - Vd = kN
@ B - Vb = kN

Inclined Reaction

@ D - Id = kN

Member Forces

kN
kN
kN
kN
Tutorial 6 - Pin Jointed Frame

For the simply supported pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & B.
  • The magnitude of the internal forces for the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ B - Hb = kN

Vertical Reactions

@ A - Va = kN
@ B - Vb = kN

Member Forces

kN
kN
kN
kN
Tutorial 7 - Pin Jointed Frame

For the simply supported pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & G.
  • The magnitude of the internal forces for the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ G - Hg = kN

Vertical Reactions

@ A - Va = kN
@ G - Vg = kN

Member Forces

kN
kN
kN
kN
Tutorial 8 - Pin Jointed Frame

For the simply supported pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & B.
  • The magnitude of the internal forces for the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ B - Hb = kN

Vertical Reactions

@ A - Va = kN
@ B - Vb = kN

Member Forces

kN
kN
kN
kN
Tutorial 9 - Pin Jointed Frame

For the given pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & G.
  • The magnitude of the internal forces for all the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ G - Hg = kN

Vertical Reactions

@ A - Va = kN
@ G - Vg = kN

Member Forces

kN
kN
kN
kN
Tutorial 10 - Pin Jointed Frame

For the simply supported pin jointed frame, calculate the following:

  • The horizontal and vertical reactions at the supports A & Q.
  • The magnitude of the internal forces for the structural members designated below.

Notes:

  • Inputs for reaction force values should be positive.
  • A positive value for a member force indicates a tie, i.e. a tension member.
  • A negative value for a member force indicates a strut, i.e. a compression member.
  • The analysis associated with this tutorial question will round all your input values to one decimal place.
Frame Data
Solution

Enter your solutions below.

Horizontal Reactions

@ A - Ha = kN
@ Q - Hq = kN

Vertical Reactions

@ A - Va = kN
@ Q - Vq = kN

Member Forces

kN
kN
kN
kN