Structural Mechanics

Question 1

Static structures?

Answer 1

Statically determinate structures (SDS)

Question 2

Hyperstatic structures?

Answer 2

Statically indeterminate structures (SIS)

Question 3

Mechanisms/ Hypostatic systems?

Answer 3

Statically deficient systems

Question 4

Structural redundancy/ Indeterminancy number (α) ?

Answer 4

The number of extra unknowns in relation to a statically determinate system

Question 5

Redundancy formula?

Answer 5

External (de) + internal (ai) redundancy

Question 6

How do hinges affect redundancy?

Answer 6

-1 redundancy for each internal hinge because it adds an equation

Question 7

What redundancy do local mechanisms have?

Answer 7

Local mechanisms can appear >_ 0 total redundancy

Question 8

How do cells affect redundancy?

Answer 8

+3* number of cells to redundancy

Question 9

How do bars in trusses that connect to existing nodes effect redundancy?

Answer 9

In a truss add redundancy for each extra bar connecting two existing nodes in a truss minus the number of internal hinges

Question 10

What external work equal to graphically?

Answer 10

The external forces undertake an external work equal to the area under the force - displacement curve up to the value of the force applied and the displacement produced

Question 11

Strain energy?

Answer 11

The energy stories in a structure through elastic deformation

Question 12

What type of energy is external work undertaken by the external loads stored as?

Answer 12

Strain energy

Question 13

d1(U)=Δd(W)

Answer 13

Virtual internal forces* real deformations = virtual external forces* real displacements

Question 14

How to work out displacements for trusses?

Answer 14

Sum of all virtual axis forces (N) x Real strains (ε) = 1* real displacement

Question 15

How to work out displacements for beams and frames?

Answer 15

Sum of all virtual bending moments (M) * Real curvatures(k) = 1 x real displacement

Question 16

Structure (SIS) = +*_

Answer 16

Structure (SIS) = Case 0 (SDS) + X1 (unknown) * Case 1 (SDS)

Question 17

Flexibility method of statically indeterminate structures ( removing supports)?

Answer 17

• Obtain the redundancy
• Identify α supports that can be removed maintaining equilibrium
• Replace the supports by the unknown reactions
• Decompound the initial structure in α+1 load cases. Apply the external loads in Case 0, and the reactions equal to 1 times the unknowns for the other α cases
• Obtain the vertical displacements at the supports that have been removed (using the unit load method, with unit loads equal to the load cases 1 to α, and applying superposition)
• Impose the compatibility equation displacement = 0 at each removed support and obtain the unkowns

Question 18

Flexibility method for statically indeterminate structures (adding hinges)?

Answer 18

• Obtain the redundancy
• Identify α hinges that can be added maintaining equilibrium
• Replace each continuous section by a hinge and the corresponding unknown bending moment (couple of moments)
• Decompound the initial structure in α+1 load cases. Apply the external loads in case 0, an a couple of unityoments times the unknowns for the other α cases
• Obtain the angular dislocations at the hinges (using the unit load method, with unit loads equal to the load cases 1 to α, and applying superposition)
• Impose the compatibility equation dislocation=0 at each added hinge , and obtain unkowns

Question 19

F1= Σ ((N0 L)/(EA) + ΔL0) N1

Answer 19

N0= axial forces in case 0 (real)
EA= youngs modulus*area
L= length of beam
ΔL = change in length
N1= axial force in case 1
F1= unknown force

Question 20

F2= Σ ((N1)^2* L)/EA

Answer 20

E= Young’s modulus
A= area
N1= Axial force of case 1
L= length of beam

Question 21

F1 + F2 * X1 = 0

Answer 21

X1= unknown force

Question 22

What is the product integral of two rectangles?

Answer 22

Lab

Length* height of one rectangle * height of second rectangle

Question 23

What is the product integral of a triangle and rectangle?

Answer 23

1/2 * L * a * b

L= length
a= height of triangle
b= height of rectangle

Question 24

What is the product integral of two triangles?

Answer 24

1/3 * L * a * b

L= length
a= height of triangle one
b= height of triangle two

Question 25

What is the product integral of two triangles in opposite directions?

Answer 25

1/6 L a b

Length * height of one triangle * height of two triangle

Question 26

What is the product integral of a not right angled triangle and a right angle triangle ?

Answer 26

1/4 Lab

L= length
a= height of one triangle
b= height of second triangle

Question 27

What is the product integral of a rectangle and semi circle?

Answer 27

2/3 Lab

Length* height of rectangle * radius