Cycling is becoming an increasingly popular form of entertainment and transportation. Moreover, cycling has become a very popular competitive sport among both amateurs and professional athletes. Whether bicycles are used for recreation, transportation or competition, the bicycle industry is constantly improving the various components of the bicycle as well as the bicycle frame. The bicycle crank arm is one component that has been heavily redesigned. In recent years, some cyclists have become particularly fond of very hard riding in the mountains. When riding in the mountains, various components can often be damaged. One particular component that sometimes breaks due to this very hard riding in the mountains is the bicycle crank arm. Because the bicycle crank arm is rotatably connected between the pedal and the bottom bracket, when the pedal hits external objects such as rocks, trees, and artificial objects, the bicycle crank arm is usually subjected to strong external forces from the pedal. Moreover, in recent years, in order to reduce weight, bicycle crank arms are made of lightweight materials such as aluminum. As a result, these forces often cause damage, such as bending and breaking the crank arm of this lightweight bicycle. Therefore, the bicycle crank arm assembly often includes a reinforcing member connected to the bicycle crank arm at the part to which the pedal shaft is connected. Reinforcement members are usually made of rigid materials, such as steel, to ensure the rigidity of the connection between the pedal and the bicycle crank arm. An example of such a reinforcing member includes a bushing member inserted into the pedal connection hole of the bicycle crank arm for connection to the pedal shaft of the pedal. The reinforcing member comprises a thread formed on an outer surface and an inner surface of the bushing member. The thread on the peripheral surface of the bushing member is engaged with the thread on the inner surface of the pedal connection hole of the bicycle crank arm. The thread on the inner surface of the bushing member is engaged with the thread of the pedal shaft. In other words, the stiffener is screwed into the pedal connection hole of the crank arm, and the pedal shaft is screwed into the stiffener. However, due to the inherent clearance of the thread, the structural arrangement of this conventional reinforcing member will increase the clearance of the connection between the bicycle crank arm and the pedal shaft. When external forces are applied to the crank arm through the pedal, this clearance at the connection between the crank arm and the pedal often causes damage to the bicycle crank arm, such as bending and cracking.