# Problem 654 | Beam Deflection by Conjugate Beam Method

**Problem 654**

For the beam in Fig. P-654, find the value of EIδ at 2 ft from R_{2}.

# Problem 653 | Beam Deflection by Conjugate Beam Method

**Problem 653**

Compute the midspan value of EIδ for the beam shown in Fig. P-653. (Hint: Draw the M diagram by parts, starting from midspan toward the ends. Also take advantage of symmetry.

# 01 - Highest point of projectile as measured from inclined plane

**Problem 01**

A projectile is fired up the inclined plane at an initial velocity of 15 m/s. The plane is making an angle of 30° from the horizontal. If the projectile was fired at 30° from the incline, compute the maximum height z measured perpendicular to the incline that is reached by the projectile. Neglect air resistance.

# Conjugate Beam Method | Beam Deflection

Deflection on real beam = Moment on conjugate beam

### Properties of Conjugate Beam

Engr. Christian Otto Mohr

- The length of a conjugate beam is always equal to the length of the actual beam.
- The load on the conjugate beam is the M/EI diagram of the loads on the actual beam.

# Strain Energy Method (Castigliano’s Theorem) | Beam Deflection

Engr. Alberto Castigliano

Italian engineer Alberto Castigliano (1847 – 1884) developed a method of determining deflection of structures by strain energy method. His *Theorem of the Derivatives of Internal Work of Deformation* extended its application to the calculation of relative rotations and displacements between points in the structure and to the study of beams in flexure.

# 1012 Train at constant deceleration | Rectilinear Translation

**Problem 1012**

A train moving with constant acceleration travels 24 ft (7.32 m) during the 10^{th} sec of its motion and 18 ft (5.49 m) during the 12^{th} sec of its motion. Find its initial velocity and its constant acceleration.

# 02 Problem involving angle and median | Properties of a Triangle

**Problem 02**

From the figure shown below, angle CAD = angle BCD = theta and CD is a median of triangle ABC through vertex C. Determine the value of the angle theta.

# 10 Solving for angle A in triangle ABC

**Problem 10**

In a triangle ABC, if $\dfrac{2 \cos A}{a} + \dfrac{\cos B}{b} + \dfrac{2 \cos C}{c} = \dfrac{a}{bc} + \dfrac{b}{ca}$, find the value of angle $A$.

# Problem 10 | Special Products and Factoring

**Problem 10**

Given that $x + y + xy = 1$, where $x$ and $y$ are nonzero real numbers,find the value of $xy + \dfrac{1}{xy} - \dfrac{y}{x} - \dfrac{x}{y}$.