Structural Analysis Test 1

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Structural Analysis Test 1

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Question 1
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Pick the incorrect statement among the following regarding Influence line diagram (ILD):

A
ILD can be drawn for statically determinate as well as indeterminate structures.

B
ILD for determinate structure is linear always.

C
ILD for an indeterminate structure can be either linear or nonlinear.

D
There can be infinite number of ILD drawn for a particular beam.

Solution

An influence line represents the variation of either the reaction, shear, moment, or deflection at a specific point in a member as a concentrated force moves over the member.
Advantages of drawing ILD are as follows:
i) To determine the value of quantity (shear force, bending moment, deflection, etc.) for a given system of loads on the span of structure.
ii) To determine the position of a live load for the quantity to have the maximum value and hence to compute the maximum value of the quantity.
ILD can be drawn for statically determinate as well as indeterminate structures. ILD for statically determinate and indeterminate structures are linear and nonlinear respectively.
Infinite numbers of ILD can be drawn for a particular structural member for computing different quantity at different sections.
Question 2
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Which of the following is not true regarding assumptions made for matrix method of structural analysis?

A
Materials of all the structural member obeys Hooke’s Law

B
Frames members are inextensible

C
It is applicable for both determinate as well as indeterminate structure

D
Change in length under a deflection perpendicular to member length is zero

Solution

Flexibility matrix method and stiffness matrix method are two matrix methods.
Following are the assumptions made for matrix analysis of the structure:
a) Material of all the structural member obeys Hooke’s law.
b) Members are subjected to small deflections.
c) Change in length under a deflection perpendicular to member length is 0.
d) Principal of superposition is applicable.
e) Frames – members are considered to be inextensible.
Question 3
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The flexibility matrix for a beam is given as \(\left| {\begin{array}{*{20}{c}} b&a\\ d&c \end{array}} \right|,\) which of the following represent the correct relation between b and c, given that b and c are non-zero real numbers.

A
b = c, b < 0, c < 0

B
b ≠ c, b > 0, c > 0

C
a = d, b > 0, c < 0

D
a = d, b > 0, c > 0

Solution

Concept:
The flexibility matrix has the following two main properties:
1. The flexibility matrix is square symmetric matrix due to Maxwell’s reciprocal theorem which me Ans: that its diagonal elements are always equal.
2. The diagonal elements of flexibility matrix are always positive due to Castigilanostheorem–II.
Calculation:
a = d (using 1st property)
b > 0 and c > 0 (using 2nd property)
∴ b = c, b > 0, c > 0