Structural Mechanics

Question 1

Structural redundancy/ Indeterminancy number (α) ?

Answer 1

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

Question 2

Redundancy formula?

Answer 2

External (de) + internal (ai) redundancy

Question 3

How do hinges affect redundancy?

Answer 3

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

Question 4

What redundancy do local mechanisms have?

Answer 4

Local mechanisms can appear >_ 0 total redundancy

Question 5

How do cells affect redundancy?

Answer 5

+3* number of cells to redundancy

Question 6

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

Answer 6

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

Question 7

d1(U)=Δd(W)

Answer 7

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

Question 8

How to work out displacements for trusses?

Answer 8

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

Question 9

How to work out displacements for beams and frames?

Answer 9

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

Question 10

Structure (SIS) = +*_

Answer 10

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

Question 11

Flexibility method of statically indeterminate structures ( removing supports)?

Answer 11

• 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 12

Flexibility method for statically indeterminate structures (adding hinges)?

Answer 12

• 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 13

F1= Σ ((N0 L)/(EA) + ΔL0) N1

Answer 13

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 14

F2= Σ ((N1)^2* L)/EA

Answer 14

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

Question 15

F1 + F2 * X1 = 0

Answer 15

X1= unknown force

Question 16

What is the product integral of two rectangles?

Answer 16

Lab

Length* height of one rectangle * height of second rectangle

Question 17

What is the product integral of a triangle and rectangle?

Answer 17

1/2 * L * a * b

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

Question 18

What is the product integral of two triangles?

Answer 18

1/3 * L * a * b

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

Question 19

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

Answer 19

1/6 L a b

Length * height of one triangle * height of two triangle

Question 20

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

Answer 20

1/4 Lab

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

Question 21

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

Answer 21

2/3 Lab

Length* height of rectangle * radius