Structures 1 Notes PDF

# Method of Resolution and Composition of Forces ## Force - The external energy required to move the body from one place to another. - Force is a vector quantity. - SI units → Newton, kg. km. - 1 kg = 9.8 N - 1 kN = 1000 N ## Types of forces: 1. **Horizontal force:** (or) the force which acts al...

# Method of Resolution and Composition of Forces ## Force - The external energy required to move the body from one place to another. - Force is a vector quantity. - SI units → Newton, kg. km. - 1 kg = 9.8 N - 1 kN = 1000 N ## Types of forces: 1. **Horizontal force:** (or) the force which acts along the x-axis & parallel to the ground. 2. **Vertical force:** the force which acts along the y-axis and perpendicular to the ground. 3. **Inclined force:** the force that is neither along the x-axis nor along the y-axis. ## Force Nature: - **Outward from the point (Pull)** - **Towards the point (Push)** - **Compressive force** - **Tensile force** ## Resolution Resolution is the process of finding out the number of components of a single force ## Finding the Resultant Magnitude and Position for a given force system **Procedure:** 1. **Magnitude:** - R = √ ΣFx² + ΣFy² 2. **Direction:** - θ = tan⁻¹|ΣFy/ ΣFx| 3. **Position** ## Example 1: - **ΣFx:** 10 + 15 cos 60 - 25 cos 30 = 5.849 N. - **ΣFy:** 30 + 15 sin 60 + 25 sin 30 = 55.49 N. - **R:** √5.849² + 55.49² = 55.797 N. - **θ:** tan⁻¹ |55.49 /5.849| = 83.982° **Resultant lies in the 1st quadrant. (++)** - **R = 55.79 FN.** ## Example 2: - **ΣFx:** 300 + 400 cos 30 + 600 cos 50 - 1200 cos 65 = 504.94 N. - **ΣFy:** 800 - 1200 sin 65 + 400 sin 30 - 600 sin 50 = -547.196 N. - **R:** √504.94² + 547.196² = 758.277 N. - **θ:** tan⁻¹ |547.196/ 504.94| = 46.189° **ΣFx is +ve and ΣFy is -ve** Therefore, the resultant lies in the 4th quadrant. - **R = 798.277 N.** # Equillibrium Conditions and Support Reactions ## Types of Supports The different types of supports and reactions developed at these supports are as follows: 1. **Simple Support**: A simple support is set up so that the member rests on an external structure. They are able to restrain vertical forces but there is no resistance for horizontal forces and rotation. 2. **Roller Support**: Roller supports are free to rotate and translate along the surface upon which the roller acts. The surface can be horizontal, vertical (or) inclined at an angle. 3. **Hinged (or) Pinned Support**: These supports can resist both horizontal as well as vertical force but not moment. 4. **Fixed Support**: A fixed support can resist both horizontal and vertical forces, as well as moment. They restrain both rotation and translation. They are also known as rigid supports. ## Types of Beams 1. **Cantilever Beam**: This is a beam fixed at one end and free at the other end. 2. **Propped Cantilever**: A propped cantilever is a beam fixed at one end and roller at the other end. 3. **Beam with one hinged and other end on roller**: 4. **Beams with both the ends hinged**: 5. **Overhanging on one side**: When the beam is extended beyond the support on one side, it is called as overhanging on one side. 6. **Overhanging both sides** A beam which is extended beyond the supports on either side is called an overhanging on both sides. 7. **Continuous Beam**: A beam which has more than 2 supports is called a continuous beam. ## Types of Load 1. **Point load/ Concentrated load**: A point load is a load applied to a single specific point on a structural member. 2. **Uniformly Distributed load (UDL)**: A load which has got some intensity over a considerable length is called as UDL. 3. **Uniformly Varying Load(UVC)**: If the intensity of the load increases linearly along length is called as UVC.