FINAL EXAMINATION IN STRUCTURAL THEORY
Structure Imposed Loading
GIVEN: L E I
(m) (GPa) (mm4) (kN/m)
3.1 200 240x106 10.0
Double Integration Method
Situational 1 - A simply supported beam with triangular load is shown in the figure below.
Let W1 be the load per unit length, L the length, E the modulus of elasticity,
and I the moment of inertia.
1. Determine the Reactions in kN,
2. Determine the maximum bending moment and its location in kN.m & m,
3. Determine the Transverse Shear Force and its location in kN & m,
4. Determine the maximum deflection and its location in mm & m,
5. Determine the slopes in degrees,
Area Moment Method
Situational 2 - A simply supported beam with uniform distributed load is shown in the figure below.
Let W be the load per unit length, L the length, E the modulus of elasticity,
and I the moment of inertia.
1. Determine the Reactions in kN,
2. Determine the maximum bending moment and its location in kN.m & m,
3. Determine the Transverse Shear Force and its location in kN & m,
4. Determine the maximum deflection and its location in mm & m,
5. Determine the slopes in degrees,
Three Moment Equation Method
Situational 3 – For the continuous beam shown below. Determine the moments and reactions. Draw the shear and moment diagrams.
Structure Imposed Loading
L1 L2 L3 W
GIVEN: (m) (m) (m) (kN/m) (kN)
3.1 3.1 1.1 16.0 1.0
Moment Distribution Method
Situational 4 – For the continuous beam shown below. Determine the moments and reactions. Draw the shear and moment diagrams.
Structure Imposed Loading
GIVEN: L1 L2
(m) (m) (kN/m) (kN/m)
3.1 3.1 9.0 3.0
Superposition Method
Situational 5 – The beam in Figure below is supported at the right end by spring. Determine the vertical reaction at the spring support.
Structure Imposed Loading
GIVEN: L E I k
(m) (GPa) (mm4) (kN/m) (N/m)
3.1 10.0 85x106 60.0 480
Situational 6 – The beam in Figure below is supported at the right end by spring. Use k = 500 N/m, E = 22,000 MPa.
I = Moment of Inertia of Beam Section in mm4
Structure Imposed Loading
GIVEN: L E I
(m) (GPa) (mm4) (kN/m)
3.1 200 240x106 10.0
Double Integration Method
Situational 1 - A simply supported beam with triangular load is shown in the figure below.
Let W1 be the load per unit length, L the length, E the modulus of elasticity,
and I the moment of inertia.
1. Determine the Reactions in kN,
2. Determine the maximum bending moment and its location in kN.m & m,
3. Determine the Transverse Shear Force and its location in kN & m,
4. Determine the maximum deflection and its location in mm & m,
5. Determine the slopes in degrees,
Area Moment Method
Situational 2 - A simply supported beam with uniform distributed load is shown in the figure below.
Let W be the load per unit length, L the length, E the modulus of elasticity,
and I the moment of inertia.
1. Determine the Reactions in kN,
2. Determine the maximum bending moment and its location in kN.m & m,
3. Determine the Transverse Shear Force and its location in kN & m,
4. Determine the maximum deflection and its location in mm & m,
5. Determine the slopes in degrees,
Three Moment Equation Method
Situational 3 – For the continuous beam shown below. Determine the moments and reactions. Draw the shear and moment diagrams.
Structure Imposed Loading
L1 L2 L3 W
GIVEN: (m) (m) (m) (kN/m) (kN)
3.1 3.1 1.1 16.0 1.0
Moment Distribution Method
Situational 4 – For the continuous beam shown below. Determine the moments and reactions. Draw the shear and moment diagrams.
Structure Imposed Loading
GIVEN: L1 L2
(m) (m) (kN/m) (kN/m)
3.1 3.1 9.0 3.0
Superposition Method
Situational 5 – The beam in Figure below is supported at the right end by spring. Determine the vertical reaction at the spring support.
Structure Imposed Loading
GIVEN: L E I k
(m) (GPa) (mm4) (kN/m) (N/m)
3.1 10.0 85x106 60.0 480
Situational 6 – The beam in Figure below is supported at the right end by spring. Use k = 500 N/m, E = 22,000 MPa.
I = Moment of Inertia of Beam Section in mm4
