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CVE 509: ADVANCED STRUCTURAL ANALYSIS
ASSIGNMENT 1
OBOT, OFONIME GABRIEL
12/ENG03/034
To be submitted to
ENGR. JOHN WASIU
THE DEPARTMENT OF CIVIL ENGINEERING,
AFE BABALOLA
UNIVERSITY, ADO- EKITI, EKITI STATE
IN PARTIAL FULFILMENT OF
THE REQUIREMENT FOR THE AWARD OF
BACHELOR OF ENGINEERING (B.Eng.) DEGREE IN
CIVIL ENGINEERING
November 13, 2016
Question 1: Explain the advantages and disadvantages of the slope deflection
method.
Slope deflection method is a displacement or equilibrium or stiffness method. It
consists of series of simultaneous equations expressing the relation of moments
acting at the ends of the members in terms of slope and deflection. The slope
deflection equation along with equilibrium equation gives the values of unknown
rotations of the joints. Knowing these rotations, end moments are calculated using
the slope deflection equation.
ADVANTAGES OF SLOPE DEFLECTION METHOD
a. The slope-deflection method is ideal for doing calculations on continuous
beams as the equations do not become more complicated as the number of
unknowns increases. The equations remain easy to derive no matter how many
degrees of indeterminacy there are in the structure.
b. This method provides a base of knowledge that is needed to perform the
matrix-stiffness method, which is the method used to evaluate structures in
many electronic solutions.
DISADVANTAGES OF SLOPE DEFLECTION METHOD
a. The solution of simultaneous equation makes the method tedious for annual
computations.
b. The formulation of equilibrium conditions tends to be a major constraint in
adopting this method. Hence flexibility coefficients & slope displacement
methods have limited applications in the analysis of frames. While other
methods like iterative or approximate methods are used for analyzing frames
containing larger indeterminacy.
Question 2: State the procedure for the analysis of continuous beam using the slope
deflection method.
(i). Identify the degrees of freedom of the structure. For continuous beams, the degrees of freedom
consist of the unknown rotations of the joints.
(ii). Compute fixed-end moments. For each member of the structure, evaluate the fixed end
moments due to the external loads. The counterclockwise fixed-end moments are considered to be
positive.
(iii). In the case of support settlements, determine the rotations of the chords of members
adjacent to the supports that settle by dividing the relative translation between the two
ends of the member by the member length (The chord rotations are measured from the
undeformed (horizontal) positions of members, with counter- clockwise rotations considered as
positive.
(iv). Write slope-deflection equations. For each member, apply the following equation
to write two slope-deflection equations relating member end moments to the unknown
rotations of the adjacent joints.
Mnf = (+ + FEMnf
in which the subscript n refers to the near end of the member where the moment Mnf acts
and the subscript f identifies the far (other) end of the member.
(v). Write equilibrium equations. For each joint that is free to rotate, write a moment
equilibrium equation, in terms of the moments at the member ends connected to the
joint. The total number of such equilibrium equations must be equal to the number of
degrees of freedom of the structure.
(vi). Determine the unknown joint rotations. Substitute the slope- deflection equations into the
equilibrium equations, and solve the resulting system of equations for the unknown joint rotations.
(vii). Calculate member end moments by substituting the numerical values of joint rotations
determined in step 6 into the slope-deflection equations. A positive answer for an end moment
indicates that its sense is counterclockwise, whereas a negative answer for an end moment implies
a clockwise sense.
(viii). To check whether or not the solution of simultaneous equations was carried out correctly in
step (vi), substitute the numerical values of member end moments into the joint equilibrium
equations developed in step (v). If the solution is correct, then the equilibrium equations should be
satisfied.
(ix). Compute member end shears. For each member,
(a) draw a free- body diagram showing the external loads and end moments and
(b) apply the equations of equilibrium to calculate the shear forces at the ends of the
member.
(x). Determine support reactions by considering the equilibrium of the joints of the structure.
(xi). To check the calculations of member end shears and support re- actions, apply the
equations of equilibrium to the free body of the entire structure. If the calculations have
been carried out correctly, then the equilibrium equations should be satisfied.
(xii). Draw shear and bending moment diagrams of the structure by using the beam sign
convention.