China
Africa
Explore chapters and articles related to this topic
Space Statically Determinate Trusses
Published in A.I. Rusakov, Fundamentals of Structural Mechanics, Dynamics, and Stability, 2020
Now, let the totality of moment axes in conditions (10.6) make up the edges of the prism’s base ABC and its lateral edges AD1, BD2, CD3 (Figure 10S.1b). We prove that relations of force balance (10.5) follow from conditions (10.6). The first step of the proof doesn’t differ from the previous one; the force system has a resultant with the line of action running through vertex A. At the second step, we establish equality to zero for the resultant by negative proof: In order for its moment be zero relative to axis BC, it should belong to facet ABC. In order for its moment to be zero relative to axis CD3, it should belong to facet AD1D3C. To belong to both these facets, the resultant should be directed along edge AC. But in this case, it doesn’t lie in the same plane with axis BD2, about which its moment is also assumed to be zero. Hence, the resultant is zero and the given force system is balanced. Thus, the conclusion: equation sets (10.5) and (10.6) are equivalent.
Mechanics of Elastic Waves – Linear Analysis
Published in Kundu Tribikram, Mechanics of Elastic Waves and Ultrasonic Nondestructive Evaluation, 2019
In all equations derived above it is assumed that the body is in static equilibrium. Therefore the resultant force acting on the body is equal to zero. If the body is subjected to a nonzero resultant force, then it will have an acceleration u¨ (time derivatives are denoted by dots over the variable, two dots mean double derivative) and the equilibrium equation (Eq.1.24) will be replaced by the following governing equation of motion, σij,j+fi=ρu¨i
Rigging and Material Handling Safety
Published in Frank R. Spellman, Kathern Welsh, Safe Work Practices for Wastewater Treatment Plants, 2018
Frank R. Spellman, Kathern Welsh
Frequently, two or more forces act together to produce the effect of a single force, called a resultant. This resolution of forces can be explained by either the triangle law or the parallelogram law. The triangle law provides that if two concurrent forces are laid out vectorially with the beginning of the second force at the end of the first, the vector connecting the beginning and the end of the forces represents the resultant of the two forces (see Figure 16.2A). The parallelogram law provides that if two concurrent forces are laid out vectorially, with either forces pointing toward or both away from their point of intersection, a parallelogram represents the resultant of the force. The concurrent forces must have both direction and magnitude if their resultant is to be determined (see Figure 16.2B). If the individual forces are known or if one of the individual forces and the resultant are known, the resultant force may be simply calculated by either the trigonometric method (sines, cosines, and tangents) or the graphic method (which involves laying out the known force, or forces, at an exact scale and in the exact directions in either a parallelogram or triangle and then measuring the unknown to the same scale).
Experimental study on short-crested random wave interaction with pile group in double-row side-by-side arrangement: a statistical analysis
Published in Coastal Engineering Journal, 2020
Haochen Zhang, Shuxue Liu, Jinxuan Li, Yuping Fan
As aforementioned, the generation mechanism of inline and transverse force is different. But they act on structures at the same time. So the resultant force on a structure is an important factor to be concerned in engineering design. Because the inline force and transverse force are simultaneously measured; thus, the resultant force Fr,1/3 can be calculated by their vector summation. Similarly, the significant values of Fr,1/3 are used for its statistical analysis. To identify the relationship between Fr,1/3 and its associated Fx,1/3, the ratios of Fr,1/3 to Fx,1/3 on single piles in the group are analyzed. Figure 16 gives their variations versus KCLD1/3 number. It can be observed that the ratios generally increase with increasing KCLD1/3 numbers. The ratios of Fr,1/3 to Fx,1/3 on the edge piles (A1 and B1) acted by long-crested random waves take the largest values for the small cases of S/D. This is because the transverse force acting on the edge piles (A1 and B1) subject to long-crested random waves is large and it makes a big contribution to the resultant force. With the relative pile distance S/D becoming big, the ratios apparently increase with increasing standard deviation σθ.
Inverse dynamics, joint reaction forces and loading in the musculoskeletal system: guidelines for correct mechanical terms and recommendations for accurate reporting of results
Published in Sports Biomechanics, 2021
A net or a resultant force is the vector sum of a number of forces. The JRF components RX and RY are equal and opposite to the sum of all the forces acting on or parallel to the X and Y axes so, by definition, they are net or resultant forces irrespective of the inversed dynamics approach used. For example, the RY whether calculated through the Actual Forces (RY = −54 N) or Resultant Moments (RY = 39.2 N) approach is equal and opposite to the net or resultant of all the other shear (Y-axis) forces. All JRFs are also, by definition, intersegmental (acting between or across segments) because they are caused as a reaction to the forces (action) applied by the segment analysed to the adjacent segment, but this is irrespective of the inverse dynamics approach followed. For example, the contact forces RX and RY are reactions (equal and opposite) to the forces applied by the lower leg to the adjacent segment (upper leg) so they are equilibrant forces in structural mechanics terminology. The detailed FBD for the above Actual Forces approach example is shown again in Figure 3 but with the reaction force vectors RX and RY drawn to scale and pointing in the actual direction they are acting since their magnitude and direction (sign) were calculated above. The joint reaction force R is thus resolved to its components RX and RY along the two orthogonal reference frame axes X and Y that align with the long axis of the segment (compressive axis) and the shear axis, respectively, with the origin of the reference frame at the joint centre.
Quantitative analysis of extra load-carrying mechanisms to prevent progressive collapse of reinforced concrete buildings
Published in Structure and Infrastructure Engineering, 2022
Min Huang, Hua Huang, Chunliang Xue, Mengxue Guo
is the horizontal force provided by the external boundary of the structure. Similar to the BC and FP structures, the entire progressive collapse process of a BSC structure can also be divided into three cases: being a compressive force, and being a tensile force. When the external resultant force is zero.