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Determine the moments at A,B, and C, then draw the moment diagram for the beam. The moment of inertia of each span is indicated in the figure. Assume the support at B is a roller and A and C are fixed. E = 29(10^{3}) ksi.

The moments at A, B, and C, and to draw the moment diagram for the beam.

## Answer to Problem 11.1P

The moment at A for member AB is,

The moment at B for member BA is,

The moment at B for member BC is,

The moment at C for member CB is,

The following figure shows the moment diagram of the beam.

### Explanation of Solution

**Calculation:**

The following figure shows the beam diagram.

Figure-(1)

Calculate the fixed end moments at every end as shown below.

Calculate fixed end moments of member AB.

Here, given load is

Substitute

Calculate fixed end moments of member BA.

Substitute

Calculate fixed end moments of member BC.

Substitute

Calculate fixed end moments of member CB.

Substitute

Calculate the member relative stiffness factors on either side of B.

Calculate relative stiffness of member BA.

Here,

Substitute

Calculate relative stiffness of member BC.

Substitute

Calculate the distribution factors for different members.

Calculate distribution factors for AB.

Calculate distribution factors for BA.

Substitute

Substitute

Calculate distribution factors for BC.

Substitute

Substitute

Calculate distribution factors for CB.

Calculate the balance moment for each member as shown below.

Calculate balance moment foe BA.

Calculate balance moment for BC.

Draw the moment distribution table as shown below.

Joints | A | B | C | |

Member | AB | BA | BC | CB |

DF | | | | |

FEM | | | | |

Balance | - | | | - |

Carry over moment | | | | |

Balance | | | | |

| | | | |

Consider the section AB as shown below.

Figure-(2)

Write the Equation for sum of vertical forces.

Here, vertical reaction at A and B are

Write the Equation for sum of moment about A.

Substitute

Calculate the distance at which shear force changing its sign for maximum moment.

Write the Equation for shear force at distance

Equate the value of shear force to zero for distance.

Calculate the value of maximum moment at a distance of

Consider the section BC as shown below.

Figure-(3)

Write the Equation for sum of vertical forces.

Write the Equation for sum of moment about B.

Here, vertical reaction at C is

Substitute

For member BC, moment will be maximum at the center.

Calculate maximum moment at the center of BC.

**Conclusion:**

The moment at A for member AB is,

The moment at B for member BA is,

The moment at B for member BC is,

The moment at C for member CB is,

The following diagram shows the moment diagram of the beam.

Figure-(4)

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Structural Analysis (10th Edition)

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